Breaking Bad: Priorities, Intentions and Responsibility in High Performance Computing

Action expresses priorities.

― Mahatma Gandhi

Being the successful and competent at high performance computing (HPC) is an essential enabling technology for supporting many scientific, military and industrial activities. It plays an important role in national defense, economics, cyber-everything and a measure of National competence. So it is important. Being the top nation in high performance computers is an important benchmark in defining national power. It does not measure overall success or competence, but rather a component of those things. Success and competence in high performance computing depends on a number of things including physics modeling and experimentation, applied mathematics, many types of engineering including software engineering, and computer hardware. In the list of these things computing hardware is among the least important aspects of competence. It is generally enabling for everything else, but hardly defines competence. In other words, hardware is necessary and far from sufficient.

Claiming that you are what you are not will obscure the strengths you do have while destroying your credibility.

― Tom Hayes

Being a necessity for competence, hardware must receive some support for national success. Being insufficient, it cannot be the only thing supported, and it is not the determining factor for HPC supremacy. In other words, we could have the very best hardware and still be inferior to the competition. Indeed the key to success in HPC has always been a multidisciplinary endeavor and predicated on a high degree of balance across the spectrum of activities needed for competence. If one examines the state of affairs in HPC, we can easily see that all this experience and previous success has been ignored and forgotten. Instead of following a path blazed by previous funding success (i.e., ASCI), we have chosen a road to success solely focused on computing hardware and its direct implications. Worse, the lessons of the past are plain and ignored by the current management. Excellence in other areas has been eschewed in favor of the hardware’s wake. The danger in the current approach is dampening progress in a host of essential disciplines in favor of a success completely dependent on hardware.

The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.

― Bertrand Russell

Unfortunately, the situation is far worse than this. If computer hardware was in an era where huge advances in performance were primed to take place, the focus might be forgivable. Instead we are in an era where advances in hardware are incredibly strained. It is easy to see that huge advances in hardware are grinding to a halt, or at least relative to the past half century. The focus of the current programs, the “exascale” initiatives, is actually the opposite. We are attempting to continue growth in computing power at tremendous cost where the very physics of computers is working against us. The focus on hardware is actually completely illogical; if opportunity were the guide hardware would be a side-show instead of the main event. The core of the problem is the complete addiction of the field on Moore’s law for approximately 50 years, and like all addicts, kicking the habit is hard. In a sense under Moore’s law computer performance skyrocketed for free, and people are not ready to see it go.

Most of us spend too much time on what is urgent and not enough time on what is important.

― Stephen R. Covey

Moore’s law is dead and HPC is suffering from the effects of withdrawal. Instead of accepting the death of Moore’s law and shifting the focus to other areas for advancements, we are holding onto it like a junkie’s last fix. In other words, the current programs in HPC are putting an immense amount of focus and resources into keeping Moore’s law alive. It is not unlike the sort of heroic measures taken to extend the life of a terminal patient. Much like the terminal patient whose death is only delayed by the heroic measures, the quality of life is usually terrible. In the same way the performance of HPC is more zombie-like than robust. Achieving the performance comes at the cost of utility and general ease of use for the computers. Moreover the nature of the hardware inhibits advances inother areas due its difficulty of use. This goes above and beyond the vast resource sink the hardware is.

The core truth of HPC is that we’ve been losing this war for twenty years, and the current effort is simply the final apocalyptic battle in war that is about to end. The bottom line is that we are in a terrible place where all progress is threatened by supporting a dying trend that has benefitted HPC for decades.

I work on this program and quietly make all these points. They fall of deaf ears because the people committed to hardware dominate the national and international conversations. Hardware is an easier sell to the political class who are not sophisticated enough to smell the bullshit they are being fed. Hardware has worked to get funding before, so we go back to the well. Hardware advances are easy to understand and sell politically. The more naïve and superficial the argument, the better fit it is for our increasingly elite-unfriendly body politic. All the other things needed for HPC competence and advances are supported largely by pro bono work. They are simply added effort that comes down to doing the right thing. There is a rub that puts all this good faith effort at risk. The balance and all the other work is not a priority or emphasis of the program. Generally it is not important or measured in the success of the program, or defined in the tasking from the funding agencies.

We live in an era where we are driven to be unwaveringly compliant to rules and regulations. In other words you work on what you’re paid to work on, and you’re paid to complete the tasks spelled out in the work orders. As a result all of the things you do out of good faith and responsibility can be viewed as violating these rules. Success might depend doing all of these unfunded and unstated things, but the defined success from the work contracts are missing these elements. As a result the things that need to be done; do not get done. More often than not, you receive little credit or personal success from pursing doing the right thing. You do not get management or institutional support either. Expecting these unprioritized, unintentional things to happen is simply magical thinking.

We have the situation where the priorities of the program are arrayed toward success in a single area that puts other areas needed for success at risk. Management then asks people to do good faith pro bono work to make up the difference. This good faith work violates the letter of the law in compliance toward contracted work. There appears to be no intention of supporting all of the other disciplines needed for success. We rely upon people’s sense of responsibility for closing this gap even when we drive a sense of duty that pushes against doing any extra work. In addition, the hardware focus levies an immense tax on all other work because the hardware is so incredibly user-unfriendly. The bottom line is a systematic abdication of responsibility by those charged with leading our efforts. Moreover we exist within a time and system where grass roots dissent and negative feedback is squashed. Our tepid and incompetent leadership can rest assured that their decisions will not be questioned.

Before getting to my conclusion, one might reasonably ask, “what should we be doing instead?” First we need an HPC program with balance between the impact on reality and the stream of enabling technology. The single most contemptible aspect of current programs is the nature of the hardware focus. The computers we are building are monstrosities, largely unfit for scientific use and vomitously inefficient. They are chasing a meaningless summit of performance measured through an antiquated and empty benchmark. We would be better served through building computers tailored to scientific computation that solve real important problems with efficiency. We should be building computers and software that spur our productivity and are easy to use. Instead we levy an enormous penalty toward any useful application of these machines because of their monstrous nature. A refocus away from the meaningless summit defined by an outdated benchmark could have vast benefits for science.

We could then free up resources to provide a holistic value stream from computing we know by experience. Real applied focusing on modeling and solution methods produces the greatest possible benefit. These immensely valuable activities are completely and utterly unsupported by the current HPC program and paid little more than lip service. Hand-in-hand with the lack of focus on applications and answers is no focus on verification or validation. Verification deals with the overall quality of the calculations, which is just assumed by the magnitude of the calculations (it used so much computer power, it has to be awesome, right?). The lack of validation underpins a generic lack of interest in the quality of the work in terms of real world congruence and impact.

Next down the line of unsupported activities is algorithmic research. The sort of algorithmic research that yields game-changing breakthroughs is unsupported. Algorithmic breakthroughs make the impossible, possible and create capabilities undreamed of. They create a better future we couldn’t even dream of. We are putting no effort into this. Instead we have the new buzzword of “co-design” where we focus on figuring out how to put existing algorithms on the monstrous hardware we are pursuing. The benefits are hardly game changing, but rather simply fighting the tidal wave of entropy of the horrific hardware. Finally we get to the place where funding exists, code development that ports existing models, methods and algorithms onto the hardware. Because little or no effort is put into making this hardware scientifically productive (in fact it’s the opposite), the code can barely be developed and its quality suffers mightily.

A huge tell in the actions of those constructing current HPC programs is their inability to learn from the past (or care about the underlying issues). If one looks at the program for pursuing exascale, it is structured almost identically to the original ASCI program, except being even more relentlessly hardware obsessed. The original ASCI program needed to add significant efforts in support of physical modeling, algorithm research and V&V on top of the hardware focus. This reflected a desire and necessity to produce high quality results with high confidence. All of these elements are conspicuously absent from the current HPC efforts. This sends two clear and unambiguous messages to anyone paying attention. The first message is a steadfast belief that the only quality needed is the knowledge that a really big expensive computer did the calculation at great cost. Somehow the mere utilization of such exotic and expensive hardware will endow the calculations with legitimacy. The second message is that no other advances other than computer power are needed.

The true message is that connection to credibility and physical reality has no importance whatsoever to those running these programs. The actions and focus of the work spelled out plainly in the activities funded makes their plans. The current HPC efforts make no serious attempt to make sure calculations are high quality or impactful in the real world. If the calculations are high quality there will be scant evidence to prove this, and any demonstration will be done via authority. We are at the point where proof is granted by immensely expensive calculations rather then convincing evidence. There will be no focused or funded activity to demonstrate quality. There will be no focused activity to improve the physical, mathematical or algorithmic basis of the codes either. In other words all the application code related work in the program is little more than a giant porting exercise. The priority and intents regarding quality are clear to those of us working on the project, namely quality is not important and not valued.

I’ve been told to assume that the leadership supports the important things to do that are ignored by our current programs. Seeing how our current programs operate, this is hardly plausible. Every single act by the leadership constructs an ever-tightening noose of planning, reporting and constraint about our collective necks. Quality, knowledge and expertise are all seriously devalued in the current era, and we can expect the results to reflect our priorities. We see a system put in place that will punish any attempt to do the right thing. The “right thing” is to do exactly what you’re told to do. Of course, one might argue that the chickens will eventually come home to roost, and the failures of the leadership will be laid bare. I’d like to think this is inevitable, but recent events seem to indicate that all facts are negotiable, and any problems can be spun through innovative marketing and propaganda into success. I have a great deal of faith that the Chinese will mop the floor with us in HPC, and our current leadership should shoulder the blame. I also believe the blame will not fall to the guilty. It never does, today; the innocent will be scapegoated for their mistakes.

Nothing in this World is Static…Everything is Kinetic..

If there is no ‘progression’…there is bound to be ‘regression’…

― Abha Maryada Banerjee

I am left with the feeling that an important opportunity for reshaping the future is being missed. Rather than admit the technological limitations we are laboring under and transform HPC towards a new focus, we continue along a path that appears to be completely nostalgic. The acceptance of the limitations in the growth of computer power in the commercial computing industry led to a wonderful result. Computer hardware shifted to mobile computing and unleashed a level of impact and power far beyond what existing at the turn of the Century. Mobile computing is vastly more important and pervasive than the computing that preceded it. The same sort of innovation could unleash HPC to produce real value far beyond anything conceivable today. Instead we have built a program devoted to nostalgia and largely divorced from objective reality.

Doing better would be simple, at least at a conceptual level. One would need to commit to a balanced program where driving modeling and simulation to impact the real world is a priority. The funded and prioritized activities would need to reflect this focus. Those leading and managing the program would need to ask the right questions and demand progress in the right areas. Success would need to be predicated on the same holistic balanced philosophy. The people working on these programs are smart enough to infer the intent of the programs. This is patently obvious by examining the funding profiles.

Programs are funded around their priorities. The results that matter are connected tomoney. If something is not being paid for it is not important. If one couples steadfast compliance with only working on what you’re funded to do, any call to do the right thing despite funding is simply comical. The right thing becomes complying, and the important thing in this environment is funding the right things. As we work to account for every dime of spending in ever finer increments, the importance of sensible and visionary leadership becomes greater. The very nature of this accounting tsunami is to blunt and deny visionary leadership’s ability to exist. The end result is spending every dime as intended and wasting the vast majority of it on shitty, useless results. Any other outcome in the modern world is implausible.

You never change things by fighting the existing reality.

To change something, build a new model that makes the existing model obsolete.

― R. Buckminster Fuller

Are We Doing Numerical Error Bars Right?

No. I don’t think so, but I’ll give my argument.

If you reject feedback, you also reject the choice of acting in a way that may bring you abundant success.

― John Mattone

Despite a relatively obvious path to fulfillment, the estimation of numerical error in modeling and simulation appears to be worryingly difficult to achieve. A big part of the problem is outright laziness, inattention, and poor standards. A secondary issue is the mismatch between theory and practice. If we maintain reasonable pressure on the modeling and simulation community we can overcome the first problem, but it does require not accepting substandard work. The second problem requires some focused research, along with a more pragmatic approach to practical problems. Along with these systemic issues we can deal with a simpler problem, where to put the error bars on simulations, or should they show a bias or symmetric error. I strongly favor a bias.

Implicit in this discussion is an assumption of convergence for a local sequence of calculations. I suspect the assumption is generally a good one, but also prone to failure. One of the key realities is the relative rarity of calculations in the asymptotic range of convergence for methods and problems of interest. The biggest issue is how problems are modeled. The usual way of modeling problems or creating models for physics in problems produces technical issues that inhibit asymptotic convergence (various discontinutiies, other singularities, degenerate cases, etc.). Our convergence theory is predicated on smoothness that rarely exists in realistic problems. This gets to the core of the shortcomings of theory, we don’t know what to expect in these cases. In the end we need to either make some assumptions, collect data and do our best, or do some focused research to find a way.

The basic recipe for verification is simple: make an assumption about the form of the error, collect calculations and use the assumed error model to estimate errors. The assumed error form is $A = S_k + C h_k^\alpha$ where $A$ is the mesh converged solution, $S_k$ is the solution on a grid $k$, $h_k$ is the mesh density, $C$ is a constant of proportionality and $\alpha$ is the convergence rate. We see three unknowns in this assumed form, $A$, $C$ and $\alpha$. Thus we need at least three solutions to solve for these values, or more if we are willing to solve an over-determined problem. At this point the hard part is done, and verification is just algebra and a few very key decisions. It is these key decisions that I’m going to ask some questions about.

The first thing to note is the basic yardstick for the error estimate is the difference between $A$ and the grid solution $S_k$, which we will call $\Delta A$.  Notice that this whole error model assumes that the sequence of solutions $S_k$ approaches $A$ monotonically as $h_k$ becomes smaller. In other words all the evidence supports the solution going to $A$. Therefore the error is actually signed, or biased by this fact. In a sense we should consider $A$ to be the most likely, or best estimate of the true solution as $h \rightarrow 0$. There is also no evidence at all that the solution is moving the opposite direction. The problem I’m highlighting today is that the standard in solution verification does not apply these rather obvious conclusions in setting the numerical error bar.

The standard way of setting error bars takes the basic measure of error, multiplies it by an engineering safety factor $C_s \ge 1$, and then centers it about the mesh solution, $S_k$. The numerical uncertainty estimate is simple, $U_s = C_s \left| \Delta A \right|$. So half the error bar is consistent with all the evidence, but the other half is not. This is easy to fix by ridding ourselves of the inconsistent piece.

The core issue I’m talking about is the position of the numerical error bar. Current approaches center the error bar on the finite grid solution of interest, usually the finest mesh used. This has the effect of giving the impression that this solution is the most likely answer, and the true answer could be either direction from that answer. Neither of these suggestions is supported by the data used to construct the error bar. For this reason the standard practice today is problematic and should be changed to something supportable by the evidence. The current error bars suggest incorrectly that the most likely error is zero. This is completely and utterly unsupported by evidence.

Instead of this impression, the evidence is pointing to the extrapolated solution as the most likely answer, and the difference between that solution, $A$, and the mesh of interest $S_k$ is the most likely error. For this reason the error bar should be centered on the extrapolated solution. The most likely error is non-zero. This would make the error biased, and consistent with the evidence. If we padded our error estimate with a safety factor, $C_s$, the error bar would include the mesh solution, $S_k$ and the potential for zero numerical error, but only as a low probability event. It would present the best estimate of the error as the best estimate.

There is a secondary impact of this bias that is no less important. The current standard approach also significantly discounts the potential for the numerical error to be much larger than the best estimate (where the current centering makes the best estimate appear to be low probability!). By centering the error bar on the best estimate we then present larger error as being equally as likely as smaller error, which is utterly and completely reasonable.

The man of science has learned to believe in justification, not by faith, but by verification.

― Thomas Henry Huxley

Why has this happened?

Part of the problem is the origin of error bars in common practice, and a serious technical difference in their derivation. The most common setting for error bars is measurement error. Here a number of measurements are taken and then analyzed to provide a single value (or values). In the most common use the mean value is presented as the measurement (i.e., the central tendency). Scientists then assume that the error bar is centered about the mean through assuming normal (i.e., Gaussian) statistics. This could be done differently with various biases in the data being presented, but truth be told this is rare, as is using any other statistical basis for computing the central tendency and deviations. This point of view is the standard way of viewing an error bar and implicitly plays in the mind of those viewing numerical error. This implicit view is dangerous because it imposes a technical perspective that does not fit numerical error.

The problem is that the basic structure of uncertainty is completely different with numerical error. A resolved numerical solution is definitely biased in its error. An under-resolved numerical solution is almost certainly inherently biased. The term under resolved is simply a matter of how exacting a solution one desires, so for the purposes of this conversation, all numerical solutions are under-resolved. The numerical error is always finite and if the calculation is well behaved, the error is always a bias. As such the process is utterly different than measurement error. With measurements there is an objective reality that is trying to be sensed. Observations can be biased, but generally are assumed to be unbiased unless otherwise noted. We have fluctuations in the observation or errors in the measurement itself. These both can have a distinct statistical nature. Numerical error is deterministic and structured, and has a basic bias through the leading order truncation error. As a result error bars from both sources should be structurally different. There are simply not the same thing and should not be treated as such.

The importance of this distinction in perspective is the proper accounting for sources and impact of uncertainty in modeling and simulation. Today we suffer most greatly from some degree of willful ignorance of uncertainty, and when it is acknowledged, too narrow a perspective. Numerical error is rarely estimated, assumed away and misrepresented even when it is computed. In the best work available, uncertainty is tackled as being dominantly epistemic uncertainty associated with modeling parameters (nominally subgrid or closure models). Large sources of uncertainty are defined by numerical error, problem modeling assumptions, model form error, and experimental uncertainty to name the big ones. All of these sources of uncertainty are commonly ignored by the community without much negative feedback, this needs to be somewhere for progress.

Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements.

― Rudolf Carnap

Dealing with Bias and Calibration in Uncertainty Quantification

It is useless to attempt to reason a man out of a thing he was never reasoned into.

― Jonathan Swift

Most of the computer modeling and simulation examples in existence are subject to bias in the solutions. This bias comes from numerical solution, modeling inadequacy, and bad assumptions to name a few of the sources. In contrast uncertainty quantification is usually applied in a statistical and clearly unbiased manner. This is a serious difference in perspective. The differences are clear. With bias the difference between simulation and reality is one sided and the deviation can be cured by calibrating parts of the model to compensate. Unbiased uncertainty is common in measurement error and ends up dominating the approach to UQ in simulations. The result is a mismatch between the dominant mode of uncertainty and how it is modeled. Coming up with a more nuanced and appropriate model that acknowledges and deals with bias appropriately would be great progress.

One of the archetypes of the modern modeling and simulation are climate simulations (and their brethren, weather). These simulations carry with them significant bias associated with lack of computational resolution. The computational mesh is always far too coarse for comfort, and the numerical errors are significant. There are also issues associated with initial conditions, energy balance and representing physics at and below the level of the grid. In both cases the models are invariably calibrated heavily. This calibration compensates for the lack of mesh resolution, lack of knowledge of initial data and physics as well as problems with representing the energy balance essential to the simulation (especially climate). A serious modeling deficiency is the merging of all of these uncertainties into the calibration with an associated loss of information.

We all see only that which we are trained to see.

― Robert Anton Wilson

The issues with calibration are profound. Without calibration the models are effectively useless. For these models to contribute to our societal knowledge and decision-making or raw scientific investigation, the calibration is an absolute necessity. Calibration depends entirely on existing data, and this carries a burden of applicability. How valid is the calibration when the simulation is probing outside the range of the data used to calibrate? We commonly include the intrinsic numerical bias in the calibration, and most commonly a turbulence or mixing model is adjusted to account for the numerical bias. A colleague familiar with ocean models quipped that if the ocean were as viscous as we modeled it, one could drive to London from New York. It is well known that numerical viscosity stabilizes calculation, and we can use numerical methods to model turbulence (implicit large eddy simulation), but this practice should at the very least make people uncomfortable. We are also left with the difficult matter of how to validate models that have been calibrated.

I just touched on large eddy simulation, which is a particularly difficult topic because numerical effects are always in play. The mesh itself is part of the model with classical LES. With implicit LES the numerical method itself provides the physical modeling, or some part of the model. This issue plays out in weather and climate modeling where the mesh is part of the model rather than independent aspect of it. It should surprise no one that LES was born from weather-climate modeling (at the time where the distinction didn’t exist). In other words the chosen mesh and the model are intimately linked. If the mesh is modified, the modeling must also be modified (recalibrated) to get the balancing of the solution correct. This tends to happen in simulations where an intimate balance is essential to the phenomena. In these cases there is a system that in one respect or another is in a nearly equilibrium state, and the deviations from this equilibrium are essential. Aspects of the modeling related to the scales of interest including the grid itself impact the equilibrium to a degree that an un-calibrated model is nearly useless.

If numerical methods are being used correctly and at a resolution where the solution can be considered remotely mesh converged, the numerical error is a pure bias error. A significant problem is the standard approach to solution verification that treats numerical error as unbiased. This is applied in the case where no evidence exists for the error being unbiased! Well-behaved numerical error is intrinsically biased. This is a significant issue because making a biased error, unbiased represents a significant loss of information. Those who either must or do calibrate their models to account for numerical error rarely explicitly estimate numerical error, but account for the bias as a matter of course. Ultimately the failure of the V&V community to correctly apply well-behaved numerical error as a one-sided bias is counter-productive. It is particularly problematic in the endeavor to deal proactively with the issues associated with calibration.

Science is about recognizing patterns. […] Everything depends on the ground rules of the observer: if someone refuses to look at obvious patterns because they consider a pattern should not be there, then they will see nothing but the reflection of their own prejudices.

― Christopher Knight

Let me outline how we should be dealing with well-behaved numerical error below. If one has a quantity of interest where a sequence of meshes produces the monotonic approach to a value (assuming the rest of the model is held fixed) then the error is well behaved. The sequence of solutions on the meshes can then be used to estimate the solution to the mathematical problem, that is the solution where the mesh resolution is infinite (absurd as it might be). Along with this estimate of the “perfect” solution, the error can be estimated for any of the meshes. For this well-behaved case the error is one sided, a bias between the ideal solution and the one with a mesh. Any fuzz in the estimate would be applied to the bias. In other words any uncertainty in the error estimate is centered about the extrapolated “perfect” solution, not the finite grid solutions. The problem with the current accepted methodology is that the error is given as a standard two-sided error bar that is appropriate for statistical errors. In other words we use a two-sided accounting for this error even though there is no evidence for it. This is a problem that should be corrected. I should note that many models (i.e., like climate or weather) invariably recalibrate after all mesh changes, which invalidates the entire verification exercise where the model aside from the grid should be fixed across the mesh sequence.

I plan to talk more about this issue next week along with a concrete suggestion about how to do better.

When we get to the heart of the matter at hand, dealing with uncertainty in calibrated models, we rapidly come to the conclusion that we need to keep two sets of books. If the first thing that comes to mind is, “that’s what criminals do,” you’re on the right track. You should feel uneasy about this conclusion, and we should all feel as sense of disease regarding this outcome. What do we put in these two books? In one case we have calibrated models, and we can rely upon this model to reliably interpolate the data it is calibrated with. So for quantities of interest used to calibrate a model, the model is basically useless, or perhaps it unveils uncertainty and inconsistency within the data used for calibration.

A model is valuable for inferring other things from simulation. It is good for looking at quantities that cannot be measured. In this case the uncertainty must be approached carefully. The uncertainty in these values must almost invariably be larger than the quantities used for calibration. One needs to look at the modeling connections for these values and attack a reasonable approach to treating the quantities with an appropriate “grain of salt”. This includes numerical error, which I talked about above too. In the best case there is data available that was not used to calibrate the model. Maybe these are values that are not as highly prized or as important as those used to calibrate. The uncertainty between these measured data values and the simulation gives very strong indications regarding the uncertainty in the simulation. In other cases some of the data potentially available for calibration has been left out, and can be used for validating the calibrated model. This assumes that the hold-out data is sufficiently independent of the data used.

A truly massive issue with simulations is extrapolation of results beyond the data used for calibration. This is a common and important use of simulations. One should expect the uncertainty to grow substantially with the degree of extrapolation from data. A common and pedestrian source for seeing what this looks like is least square fitting of data. The variation and uncertainty in the calibrated range is the basis of the estimates, but depending on the nature of the calibrated range of the data and the degree of extrapolation, the uncertainty can grow to be very large. This makes perfect reasonable sense, as one departs from our knowledge and experience, we should expect the uncertainty in our knowledge to grow.

A second issue to consider is our second set of books where the calibration is not taken quite so generously. In this case the most honest approach to uncertainty is to apply significant variation to the parameters used to calibrate the model. In addition we should include the numerical error in the uncertainty. In the case of deeply calibrated models these sources of uncertainty can be quite large and generally paint an overly pessimistic picture of the uncertainty. Conversely we have an extremely optimistic picture of uncertainty with calibration. The hope and best possible outcome is that these two views bound reality, and the true uncertainty lies between these extremes. For decision-making using simulation this bounding approach to uncertainty quantification should serve us well.

There are three types of lies — lies, damn lies, and statistics.”

― Benjamin Disraeli

Get Back In The Box

Change almost never fails because it’s too early. It almost always fails because it’s too late.

– Seth Godin

I read a lot including books, papers, articles, online content, and whatever else I can get my hands on. My interests are wide and varied including everything from deep technical science articles to more intellectual takes on popular culture. Among my interests are business or management articles. These speak about various ways of getting the best results from employees using largely positive and empowering techniques. Somehow I never see the techniques espoused in these articles in practice. Increasingly, the articles I read about management and business are science fiction with an ever-widening gap between reality and the ideal. The same gap is present in the realm of politics and public policy. Many bi-partisan forces threaten to push us into an authoritarian future that crushes human spirit challenge the ideal and progressive changes needed to make society function better. Inside and outside of work we see the potential of people constricted to produce predictable results that comply with a sense of order and safety.

When I read articles on excellence in management and business a big part of the message is employee empowerment and motivation. Empowered and motivated employees can be a huge benefit for a company (or by extension Lab, University, organization,…). Another way of expressing this common message is the encouragement of innovation and problem solving as a route to added value and high performance. Usually this is articulated as out of the box thinking, work and performance. Yet when I return to my reality, the writing seems dramatically out of touch and impossible to imagine being implemented where I work. Almost every thing my management does, and our “corporate” governance strives for is compliance, subservience, and in the box thinking. We are pushed to be predictable and downright pedestrian in everything we do. A large part of the ability to tolerate this environment is the articulation of standards of performance. Today standards of performance are defined not by excellence and achievement, but compliance and predictability. The result is the illusion of excellence and achievement when the reality is exactly the opposite. Remarkably like cattle moving to slaughter, we go along with it.

The greatest irony of the current era is the need to keep out of the box thinking under control, effectively putting it in the box. You can only be out of the box within strictly defined boundaries lest you create a situation that might not be completely under control. Of course this is a complete oxymoron and leads to the sort of ridiculous outcomes at work we all recognize. We are encouraged to be bold at work as long as we comply with all the rules and regulations. We can be bold in our thinking as long as no risks are taken. It is the theatre of the absurd. We can magically manage our way to getting all the reward without any of the risk. Bold outcomes automatically come with risk, and usually unpredictable results and unintended consequences. All of these things are completely outside the realm of the acceptable today. Our governance is all about predictably intended consequences and the entire system is devoted to control and safety. The bottom line is you can’t have the fruits of boldness, innovation and discovery without risking something and potentially courting disaster. If you don’t take risks, you don’t get the rewards, a maxim that our leaders don’t seem to understand.

One of the great sources for business articles is the well-written and respected Harvard Business Review (HBR). I know my managers read many of the same things I do. They also read business books, sometimes in a faddish manner. Among these is Daniel Pink’s excellent “Drive”. When I read HBR I feel inspired, and hopeful (Seth Godin’s books are another source of frustration and inspiration). When I read Drive I was left yearning for a workplace that operated on the principles expressed there. Yet when I return to the reality of work these pieces of literature seem fictional, even more like science fiction. The reality of work today is almost completely orthogonal to these aspirational writings. How can my managers read these things, then turn around and operate the way they do? No one seems to actually think through what implementation of these ideas would look like in the workplace. With each passing year we fall further from the ideal, more toward a workplace that crushes dreams, and simply drives people into some sort of cardboard cutout variety of behavior without any real soul.

While work is the focus of my adult world, similar trends are at work on our children. School has become a similarly structured training ground for compliance and squalid mediocrity. Standardized testing is one route to this outcome where children are trained to take tests and no solve problems. Standardized testing becomes the perfect rubric for the soulless workplace that awaits them in the adult world. The rejection of fact and science by society as a whole is another way. We have a large segment of society who is suspicious of intellect. Too many people now view educated intellectuals as dangerous and their knowledge and facts are rejected whenever they disagree with the politically chosen philosophy. This attitude is a direct threat to the value of an educated populace. Under a system where intellect is devalued, education transforms into a means of training the population to obey authority and fall into line. The workplace is subject to the same trends, compliance and authority is prized along with predictability of results. The lack of value for intellect is also present within the sort of research institutions I work at. This is because it threatens predictability of results. As a result out of the box thinking is discouraged, and the entire system is geared to keep everyone in the box. We create systems oriented toward control and safety without realizing the price paid for rejecting exploration and risk. We all live a life less rich and less rewarding as a result, and by accumulating this over society, a broad-based diminishment of results.

Be genuine. Be remarkable. Be worth connecting with.

– Seth Godin

When I see my managers reading things like HBR or Drive, I’m left wondering about how they can square their actions with the distance from what they read? My wife likes to promote “Reality-based Management,” the practical application of principles within a pragmatic approach to achievement. This is good advice that I strive to apply. There is a limit to pragmatism when the forces within society continually push us away from every ideal. Pragmatism is a force for survival and making the best of a bad situation, but there is a breaking point. When does reality become so problematic that something must change? When does the disempowering force become so great that change must occur? Perhaps we are at this point. I find myself hoping for a wholesale rejection of the forces of compliance that enslave us. Unfortunately we have rejected progressive forces nationally, and embraced the slaveholders who seek to exploit and disempower us. We have accepted being disempowered in trade for safety. Make no mistake, we have handed those who abuse the populace with a yoke and whip, and a “mandate” to turn the screws on all of us. In return we all get to be safe, and live a less rich life through the controls such safety requires.

I have to admit to myself that many people prize control and safety above all else. They are willing to reject freedom and rewards if safety can be assured. This is exactly the trade that many Americans have made. Bold, exciting and rewarding lives are traded for safety and predictable outcomes. The same thing is happening for many companies and organizations and infests work with compliance through rules and regulations. We see this play out with the reactions to terrorism. Terrorism has paved the way to massive structures of control and societal safety. It also creates an apparatus for big brother to come to fruition in a way that makes Orwell more prescient than ever. The counter to such widespread safety and control is the diminished richness of life that is sacrificed to achieve it. Lives well-lived and bold outcomes are reduced in achieving safety. I’ve gotten to the point where this trade no longer seems worth it. What am I staying safe for? I am risking living a pathetic and empty life in trade for safety and security, so that I can die quietly. This is life in the box, and I want to live out of the box. I want to work out of the box too.

The core message of my work is get in the box and don’t make waves, just do what you’re told. The message from society as a whole may be exactly the same with order, structure and compliance being prized by a large portion of the population. Be happy with what you’ve got, everything is fine. I suspect that my management is just as disempowered as I am. More deeply the issues surrounding this problem are societal. Americans are epically disempowered with many people expressing this dysfunction politically. The horror show is playing out Nationally with the election of a historically unpopular and unqualified President simply because he isn’t part of the system. The population as a whole thinks things are a mess. For roughly half the people electing an unqualified, politically incorrect, outsider seems like the appropriate response. The deeper problem is that the sort of in the box forces are not partisan at all, the right does its thing and the left does another thing, but both seek to disempower the population as a whole.

Change almost never fails because it’s too early. It almost always fails because it’s too late.

– Seth Godin

Some part of Trump’s support comes from people who just want to burn the system to the ground. Another group of people exist on the left who want the same outcome, destroy the current system. Maybe Trump will destroy the system and create a future, but I seriously doubt it. I’m guessing more of a transition to kleptocratic rule where the government actively works to loot the country for the purpose of enriching a select few. I’d prefer a much more constructive and progressive path to the future where human potential is unleashed and unlocked. Ultimately a lack of progress in fixing the system will eventually lead to something extreme and potentially violent. The bottom line is that the forces enslaving us are driven by the sort of people represented by the leadership of both political parties. The ruling class has power and money with the intent of holding and expanding it and personal empowerment of common citizens is a threat to their authority. The ruling business class and wealthy elite enjoy power through subtle subjugation of the vast populace. The populace accepts their subjugation in trade for promises of safety and security through the control of risk and danger.

For now, the message at work is get in the box by complying while not making waves and simply doing what you are told to do. No amount of reading about employee empowerment can fix the reality until there is a commitment to a different path. The management can talk till they are blue in the face about their principles, diversity, excellence, teamwork and the power of innovative out of the box thinking, but the reality is the opposite. The national reality is the same, bullshit about everyone mattering, and a truth where very few matter at all. We have handed the reins of power to those who put us in bondage, and we would have done the same if the democrats had won too. There will be real differences in what the bondage looks like, but the result is largely the same. Rather than breaking our chains, we have decided to make the bonds stronger. We can hope that people recognize the error and change course sooner rather than later. As long as we continue to prize safety and security over possibility and potential, we can expect to be disempowered.

We have so much potential waiting to be unleashed by rejecting in the box thinking. To get there we need to reject over-whelming safety, control and compliance. We need to embrace risk and possibility with the faith that our talents can lead us to a greater future powered by innovative, inspired thinking and lives well lived by empowering everyone to get out of the box.

The best way to be missed when you’re gone is to stand for something when you’re here.

– Seth Godin

Verification and Validation with Uncertainty Quantification is the Scientific Method

tl;dr : VVUQ injects the fundamentals of the scientific method into modeling and simulation. The general lack of VVUQ in HPC should cause one to question how much actual science is being done.

Modeling and simulation has been hailed by many as a third way to do science taking its place next to theory and observation as one of the pillars of practice. I strongly believe that this proposition does not bear up to scrutiny. For this to be true the advent of modeling and simulation would need to change the scientific method is some fashion; it does not. This does not minimize the importance of scientific computing, but rather puts it into the proper context. Instead of being a new way to do science, it provides tools for doing partsof science differently. First and foremost modeling and simulation enhances our ability to make predictions and test theories. As with any tool, it needs to be used with care and skill. My proposition is that the modeling and simulation practice of verification and validation combined with uncertainty quantification (VVUQ) defines this care and skill. Moreover VVUQ provides an instantiation of the scientific method for modeling and simulation. An absence of emphasis on VVUQ in modeling and simulation programs should bring doubt and scrutiny on the level of scientific discourse involved. In order to see this one needs to examine the scientific method in a bit more detail.

The Scientific Method is a wonderful tool as long as you don’t care which way the outcome turns; however, this process fails the second one’s perception interferes with the interpretation of data. This is why I don’t take anything in life as an absolute…even if someone can “prove” it “scientifically.

― Cristina Marrero

To continue our conversation we need a serious discussion of the scientific method itself. What is it? What are its parts? Who does it, and what do they do? We can then map all the activities from VVUQ onto the scientific method, proving my supposition.

In science and society, the scientific method conjures a large degree of reverence. In human discourse few basic processes have the same degree of confidence and power. The two basic activities in science are theory and observation (experiment) along with some basic actions that power each, and drive the connection between these ways of doing science. We devise theories to help explain what we experience in reality. These theories are the result of asking deep questions and proposing hypothesized mechanisms for our experience. Ultimately these theories usually take on the form of principles and mathematical structure. A theory that explains a certain view of reality can then be tested by making a prediction about something reality that has not been observed. The strength of the prediction is determined by the degree of difference between the observation that formed the basis of the theory and the test of the prediction. The greater the difference in circumstance for the experiment, the stronger the test of the theory is. Ultimately there are a great number of details and quality assessments needed to put everything in context.

One thing that modeling and simulation does for science expands the ability to make predictions for complex and elaborate mathematical models. Many theories produce elaborate and complex mathematical models, which are difficult to solve and inhibit the effective scope of predictions. Scientific computing relaxes this limitations significantly, but only if sufficient care is taken with assuring the credibility of the simulations. The entire process of VVUQ serves to provide the assessment of the simulation so that they may confidently be used in the scientific process. Nothing about modeling and simulation changes the process of posing questions and accumulating evidence in favor of a hypothesis. It does change how that relaxing limitations on the testing of theory arrives at evidence. Theories that were not fully testable are now open to far more complete examination as they now may make broader predictions than classical approaches allowed.

Science has an unfortunate habit of discovering information politicians don’t want to hear, largely because it has some bearing on reality.

― Stephen L. Burns

The first part of VVUQ, the verification, is necessary to be confident that the simulation is a proper solution of the theoretical model, and suitable for further testing. The other element of verification is error estimation from the approximate solution. This is a vastly overlooked aspect of modeling and simulation where the degree of approximate accuracy is rarely included in the overall assessment. In many cases the level of error is never addressed and studied as part of the uncertainty assessment. Thus verification plays two key roles in the scientific study using modeling and simulation. Verification acts to define the credibility of the approximate solution to the theory being tested, and an estimation of the approximation quality. Without an estimate of the numerical approximation, we possibly suffer from conflating this error with modeling imperfections, and obscuring the assessment of the validity of the model. One should be aware of the pernicious practice of simply avoiding error estimation by declarative statements of being mesh-converged. This declaration should be coupled with direct evidence of mesh convergence, and the explicit capacity to provide estimates of actual numerical error. Without such evidence the declaration should be rejected.

Verification should be a prerequisite for then examining the validity of the model, or validation. As mentioned that validation without first going through verification is prone to false positives or false negatives with a risk that numerical error will be confused with the true assessment of the theoretical model and its predictions. The issue of counting numerical error as modeling is deep and broad in modeling and simulation. A proper VVUQ process with a full breadth of uncertainty quantification must include it. Like any scientific endeavor the uncertainty quantification is needed to place the examination of models in a proper perspective. When the VVUQ process is slipshod and fails to account for the sources of error and uncertainty, the scientific process is damaged and the value of the simulation is shortchanged.

Science, my boy, is made up of mistakes, but they are mistakes which it is useful to make, because they lead little by little to the truth.

― Jules Verne

Of course, validation requires data from reality to be done. This data can come from experiments or observation of the natural world. In keeping with the theme an important element of the data in the context of validation is its quality and a proper uncertainty assessment. Again this assessment is vital for its ability to put the whole comparison with simulations in context, and help define what a good or bad comparison might be. Data with small uncertainty demands a completely different comparison than large uncertainty. Similarly for the simulations where the level of uncertainty has a large impact on how to view results. When the uncertainty is unspecified either data or simulation are untethered and scientific conclusions or engineering judgments are threatened.

It is no understatement to note that this perspective is utterly missing from the high performance computing world today and the foolish drive to exascale we find ourselves on. Current exascale programs are almost completely lacking any emphasis on VVUQ. This highlights the lack of science in our current exascale programs. They are rather naked and direct hardware-centric programs that show little or no interest in actual science, or applications. The whole program is completely hardware-focused. The holistic nature of modeling and simulation is ignored and the activities connecting modeling and simulation with reality are systematically starved of resources, focus and attention. It is not too hyperbolic to declare that our exascale programs are not about science.

The quest for absolute certainty is an immature, if not infantile, trait of thinking.

― Herbert Feign

The biggest issue in the modern view of project management for VVUQ is its injection of risk into work. We live in a world where spin and BS can easily be substituted for actual technical achievement. Doing VVUQ often results in failures by highlighting problems with modeling and simulation. One of the greatest skills in being good at VVUQ is honesty. Today it is frequently impossible to be honest about shortcomings because it is perceived as vulnerability. Stating weaknesses or limitations to anything cannot be tolerated in today’s political environment, and risks project existence because it is perceived as failure. Instead of an honest assessment of the state of knowledge and level of theoretical predictivity, today’s science prefers to make over-inflated claims and publish via press release. VVUQ runs counter to this practice if done correctly. Done properly VVUQ provides people using modeling and simulation for scientific or engineering work with a detailed assessment of credibility and fitness for purpose.

Scientific objectivity is not the absence of initial bias. It is attained by frank confession of it.

― Mortimer J. Adler

Just as science has a self-correcting nature in how the scientific method work, VVUQ is a means of self-correction for modeling and simulation. A proper and complete VVUQ assessment will produce good knowledge of strengths and weaknesses in modeling and where opportunities for improvement lie. A lack of VVUQ both highlights the lack of commitment to science in a project and its unsuitability for serious work. This assessment is quite damning to current HPC effort that have failed to include VVUQ in the efforts much less their emphasis. It is basically a declaration of intent by the program to seek results associated with spin and BS instead of a serious scientific or engineering effort. This end state is signaled by far more than merely a lack of VVUQ, but also the lack of serious application and modeling support. This simply compounds the lack of method and algorithm support that also plagues the program. The most cynical part of all of this is the centrality of application impact to the case made for the HPC programs. The pitch to the nation or the World is the utility of modeling and simulation to economic or physical security, yet the programs are structured to make sure this cannot happen, and will not be a viable outcome.

We may not yet know the right way to go, but we should at least stop going in the wrong direction.

― Stefan Molyneux

The current efforts seem to be under the impression that giant (unusable, inefficient, monstrous,…) computers will magically produce predictive, useful and scientifically meaningful solutions. I could easily declare those running these programs to be naïve and foolish, but this isn’t the case, the lack of breadth and balance in these programs is willful. People surely know better, so the reasons for the gaps are more complex. We have a complete and utter lack of brave, wise and courageous leadership in HPC. We know better, we just don’t do it.

Embracing Greater Complexity can Spur Progress in Modeling & Simulation

Complexity, therefore, results in flexibility. Increasing complexity always increases capability and adaptability.

― Jacob Lund Fisker

One of the more revealing aspects of a modeling and simulation activity is the character of every aspect of activity in terms of complexity, sophistication and emphasis. Examining the balance in terms of simplicity versus complexity, and the overall sophistication is immensely revealing. Typically the level of complexity for each aspect of an activity shows the predispositions of those involved. It also varies deeply among various philosophical groundings of the investigators. Quite often people have innate tendencies that contradict the best interests of the modeling and simulation activity. It is useful to breakup the modeling and simulation activity into a set of distinct parts to understand the texture of this more keenly.

Modeling and simulation is a deep field requiring the combination of a great number of different disciplines to be successful. It invariably requires computers to be used, so software, computer science and computer engineering is involved, but the core of value arises from the domain sciences and engineering. At the level of practical use we see need an emphasis on physics and engineering with a good bit of application-specific knowledge thrown in. Modeling activities can run the gambit between very specific technology applications to general topics like fluid or solid mechanics. The activities can be more focused on governing equations or the closure of these equations with measured physical data or elaborate modeling that coarse grains phenomenology into a lower computational cost form. It is the difference in modeling between an equation of state or coefficient of viscosity and a turbulence model, or deriving a model of a solid from a molecular dynamics simulation.

In between we see a blend of mathematics, engineering and physics providing the glue between the specific application-based modeling and the computer needed to run calculations on. As I said before, the emphasis in all of this reveals so much about the intensions of work. Today, the emphasis in modeling and simulation has been drawn away from this middle ground between the utility of modeling and simulation in applications, and the powerful computers needed to conduct the calculations. This middle ground defines the efficiency, correctness and power of modeling and simulations. A closer examination of current programs shows clearly that the applications are merely a marketing tool for buying super-powerful computers, and a way of fooling people into believing their purchase has real world value. Lost in the balance is any sense that modeling and simulation is a holistic body of work succeeding or failing on the degree of synergy derived from successful multidisciplinary collaborations. The result of the current program’s composition is a lack of equilibrium that is sapping the field of its vitality.

The current exascale emphasis is almost entirely computer hardware focused where the real world drivers are contrived and vacuous. Aside from using applications to superficially market the computers, the efforts are proportional to their proximity to the computer hardware. As a result large parts of the vital middle ground are languishing without effective support. Again we lose the middle ground that is the source of efficiency and enables the quality of the overall modeling and simulation. The creation of powerful models, solution methods, algorithms, and their instantiation in software all lack sufficient support. Each of these activities has vastly more potential than hardware to unleash capability, yet it remains without effective support. When one makes are careful examination of the program all the complexity and sophistication is centered on the hardware. The result has a simpler is better philosophy for the entire middle ground and those applications drawn into the marketing ploy.

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

― George Pólya

Examining for any emphasis on verification and validation can draw the same conclusions. There is none, support for V&V is non-existent. As I’ve said on several occasions, V&V is the scientific method embodied. If V&V is absent from the overall activity there is a lack of seriousness about scientific (or engineering) credibility and the scientific method in general. Lack of support and emphasis on V&V is extremely telling with respect to exascale. Any science or applied credibility in the resulting simulations are purely coincidental and not part of programmatic success. V&V spans the scientific enterprise and underpins the true seriousness of applicability and quality in the overall enterprise. If an activity lacks any sort of V&V focus, the true commitment to either application impact or quality results should be questioned strongly.

There is no discovery without risk and what you risk reveals what you value.

― Jeanette Winterson

Within any of these subsets of activities, the emphasis on simplicity can be immensely revealing regarding the philosophy of those involved. Turbulence modeling is a good object lesson in this principle. One can look at several approaches to studying turbulence that focus on great complexity in a single area: modeling for Reynolds averaged (RANS) flows, solution methods for astrophysics with the PPM method, or direct numerical simulation (DNS) using vast amounts of computer power, but in each area the rest of the study is simple. With RANS the combination of method, and computing sophistication is usually quite limited. Alternatively the PPM method is an immensely successful and complicated numerical method run with relatively simple models and simple meshes. DNS uses vast amounts of computer power on leading edge machines, but uses no model at all aside from the governing equations and very simple (albeit high-order) methods. As demands for credible simulations grow we need to embrace complexity in several directions for progress to be made.

Underpinning each of these examples are deep philosophical conclusions about the optimal way to study the difficult problem of turbulence. With RANS modeling there is the desire for practical engineering results and modeling driving a focus on modeling. With PPM difficult flows with shock waves drive a need to provide methods with good accuracy and great robustness tailored to precise difficulties of these flows. DNS is focused on numerical accuracy through vast meshes, computer power, and accurate numerical methods (which can be very fragile). In each case a single area is the focal point of complexity and the rest of the methodology pushes for simplicity. It is quite uncommon to find cases where the complexity is partaken in several aspects of a modeling and simulation study. There may be great benefits to do this and current research directions are undermining necessary progress.

Another important area in modeling and simulation is the analysis of the results of calculation. This rapidly gets into the business of verification, validation and uncertainty quantification (VVUQ). Again the typical study that produces refined results tends to eschew complexity in other areas. This failure to embrace complexity is holding modeling and simulation back. Some aspects of complexity are unnecessary for some application, or potentially detract from an emphasis on a more valuable complexity. For example simple meshes may unleash more complex and accurate numerical methods where geometric complexity for meshing has less value. Nonetheless, combined complexity may allow levels of quality in simulations to be achieved that currently elude us. A large part of the inhibition to embracing complexity is the risk it entails in project-based work. Again we see the current tendency to avoid project risk results in the diminishment of progress by shunning complexity where it is necessary. Put differently, it is easy to saturate the tolerance for risk in the current environment and design programs that fail for failing to attack problems with sufficient aggression.

The greatest risk is not taking any.

― Tim Fargo

For VVUQ various aspects of complexity can detract from focus significantly. For example great depth in meshing detail can potentially completely derail verification of calculations. Quite elaborate meshes are created with immense detail effectively using all the reasonable computing resources. Often such meshes cannot be trivially or meaningfully coarsened to provide well-grounded and connected simulations of the finer mesh. Then to make matters worse, the base mesh, which can be functionally refined results in a calculation too expensive to conduct. The end result is a lack of verification and error estimation, or more colloquially, a “V&V fail”. This state of affairs is so common as to transition from comedy to outright tragedy. The same dynamic often plays out with UQ work where the expensive model of interest and its cost of solution squeezes out computations needed to estimate uncertainty. A better course of action would view the uncertainty estimation holistically and balance numerical, modeling, and experimental error to find the best overall estimation of uncertainty. More importantly we could more easily produce assessments that are complete and don’t cut corners.

Another key aspect of current practice in high performance computing is the tendency to highlight only the most expensive and large calculations in computer use policies. As a result the numerous smaller calculations necessary for the overall quality of simulation-based studies are discouraged. Often someone seeking to do a good credible job of simulating needs to conduct a large number of small calculations to support a larger calculation, yet the use of the big computers punishes such use. The results are large (impressive) calculations that lack any credibility. This problem is absolutely rampant in high performance computing. This is a direct result of a value system that prizes large meaningless calculations over small meaningful calculations. The credibility and meaning of the simulation based science and engineering is sacrificed to the altar of bigger is better. This value system has perverted large swaths of the modeling and simulation community, undermines VVUQ and ultimately leads to false confidence in the power of computers.

The same issue wrecks havoc on scenario uncertainty where the experimental result has intrinsic variability and no expectation of uniqueness should exist. For many such cases single experiments are conducted and viewed as the “right” answer. Instead such experiments should be viewed as a single sample from an ensemble of potential physical results. To compound matter these experiments are either real world events, terribly expensive or dangerous, or both. Doing replicate experiments is simply not going to happen. Modeling and simulation should be leaping into this void and provide information and analysis to cover this gap. Today our modeling and simulation capability is utterly and woefully inadequate to fill this role, and the reasons are multiple. A great degree of the blame lies in the basic philosophy of the modelers, the solution of a single well-posed problem where the reality is an ensemble of ill-posed problems and a distribution of answers.

Deeper issues exist with respect to the nature of equations being solved as a mean field theory. This mean field theory effectively removes many of the direct sources of solution variability from the simulation. Each of these complexities has tremendous value for enhancing the value of modeling and simulation, but is virtually unsupported by today’s research agenda. To support such an agenda we need a broad multidisciplinary focus including a complementary experimental program centered around understanding these distributional solutions. Physics and engineering modeling would need to evolve to support closing the equations, and the governing equations themselves would need to be fundamentally altered. Finally a phenomenal amount of applied mathematics would be needed to support appropriate rigor in the analysis of the models (equations), the methods of solutions, and the algorithms.

Instead of this forward looking program that might transform simulation and modeling, we have a backwards looking program obsessed with the computers and slighting everything that produces true value with their use. All of the highest value and most impactful activities for the real world are provided almost no support. The program is simply interested in putting yesterday’s models, methods, algorithms and codes on tomorrow’s computers. Worse yet, the computer hardware focus is the least effective and least efficient way to increase our grasp on the world through modeling and simulation. For an utterly naïve and uninformed person, the supercomputer is a clear product for modeling and simulation. For the sophisticated and knowledgeable person, the computer is merely a tool, and the real product is the complete and assessed calculation tied to a full V&V pedigree.

To put this conclusion differently, high performance computing hardware is only necessary to do scientific computing that impacts the world. It is far from sufficient. The current programs are focusing on an important necessary element of modeling and simulation, but virtually ignoring a host of the sufficient activities. The consequence is a program that is incredibly inadequate to provide the value for society that it should promise.

Greatness and nearsightedness are incompatible. Meaningful achievement depends on lifting one’s sights and pushing toward the horizon.

― Daniel H. Pink

Can we overcome toxic culture before it destroys us?

Then the shit hit the fan.

― John Kenneth Galbraith

I’m an unrelenting progressive. This holds true for politics, work and science where I always see a way for things to get better. I’m very uncomfortable with just sitting back and appreciating how things are. Many who I encounter see this as a degree of pessimism since I see the shortcomings in almost everything. I keenly disagree with this assessment. I see my point-of-view as optimism. It is optimism because I know things can always get better, always improve and constantly achieve a better end state. The people who I rub the wrong way are the proponents of the status quo, who see the current state of affairs as just fine. The difference in worldview is really between my deep reaching desires for a better world versus a world that is good enough already. Often the greatest enemy of getting to a better world is a culture that is a key element of the world, as it exists. Change comes whether culture wants it or not, and problems arise when the prevailing culture is unfit for these changes. Overcoming culture is the hardest part of change, and even when the culture is utterly toxic, it opposes changes that would make things better.

I’ve spent a good bit of time recently contemplating the unremitting toxicity of our culture. We have suffered through a monumental presidential election with two abysmal candidates both despised by a majority of the electorate. The winner is an abomination of a human being clearly unfit for a public office worthy of respect. He is totally unqualified for the position he will hold, and will likely be the most corrupt person to ever hold the job. The loser was thoroughly qualified, potentially corrupt too, and would have had a failed presidency because of the toxic political culture in general. We have reaped this entire legacy by allowing the public and political institutions to whither for decades. It is arguable that this erosion is the willful effort of those charged by the public with governing us. Among the institutions that are under siege and damaged in our current era are the research institutions where I work. These institutions have cultures from a bygone era, completely unfit for the modern world yet unmoving and not evolved in the face of new challenges.

This sentiment of dysfunction applies to the obviously toxic public culture, but the workplace culture too. In the workplace the toxicity is often cloaked in tidy professional wrapper, and seems wondrously nice, decent and completely OK. Often this professional wrapper shows itself as horribly passive aggressive behavior that the organization basically empowers and endorses. The problem is not the behavior of the people in the culture toward each other, but the nature of the attitude toward work. Quite often we have this layered approach that lends a well-behaved, friendly face on the complete disempowerment of employees. Increasingly the people working in the trenches are merely cannon fodder, and everything important to work happens with managers. Where I work the toxicity of the workplace and politics collide to produce a double whammy. We are under siege from a political climate that undermines institutions and a business-management culture that undermines the power of the worker.

Great leaders create great cultures regardless of the dominant culture in the organization.

― Bob Anderson

I’m reminded of the quote “culture eats strategy” (attributed to Peter Drucker) and wonder whether or not anything can be done to cure our problems without first addressing the toxicity of the underlying culture. I’ll hit upon a couple examples of the toxic cultures in the workplace and society in general. Both of these stand in opposition to a life well led. No amount of concrete strategy and clarity of thought can allow progress when the culture opposes it.

I am embedded in a horribly toxic workplace culture, which reflects a deeply toxic broader public culture. Our culture at work is polite, and reserved to be true, but toxic to all the principles our managers promote. Recently a high level manager espoused a set of high-level principles to support: diversity & inclusion, excellence, leadership, and partnership & collaboration. None of these principles is actually seen in reality and everything about how our culture operates opposes them. Truly leading and standing for the values espoused with such eloquence by identifying and removing the barriers to their actual reality would be a welcome remedy to the normal cynical response. Instead the reality is completely ignored and the fantasy of living to such values is promoted. It is not clear whether the manager knows the promoted values are fiction, or simply exists in a disconnected fantasy world. Either situation is utterly damning. The manager either knows the values are fiction, or they are so disconnected from reality that they believe the fiction. The end result is the same, no actions to remove the toxic culture are ever taken and the culture’s role in undermining values is not acknowledged.

In a starkly parallel sense we have an immensely toxic culture in our society today. The two toxic cultures certainly have connections, and the societal culture is far more destructive. We have all witnessed the most monumental political event of our lives resulting directly from the toxic culture playing out. The election of a thoroughly toxic human being as President is a great exemplar of the degree of dysfunction today. Our toxic culture is spilling over into societal decisions that may have grave implications for our combined future. One outcome of the toxic societal choice could be a sequence of events that will induce a crisis of monumental proportions. Such crises can be useful in fixing problems and destroying the toxic culture, and allowing its replacement by something better. Unfortunately such crises are painful, destructive and expensive. People are killed. Lives are ruined and pain is inflicted broadly. Perhaps this is the cost we must bear in the wake of allowing a toxic culture to fester and grow in our midst.

Reform is usually possible only once a sense of crisis takes hold…. In fact, crises are such valuable opportunities that a wise leader often prolongs a sense of emergency on purpose.

― Charles Ruhig

Cultures are usually developed, defined and encoded through the resolution of crisis. In these crises old cultures fade being replaced by a new culture that succeeds in assisting the resolution of the crisis. If the resolution of the crisis is viewed as a success, the culture becomes a monument to that success. People wishing to succeed adopt the cultural norms and re-enforce the culture’s hold. Over time such cultural touchstones become aged and incapable of dealing with modern reality. We see this problem in spades today either in the workplace or society-wide. The older culture in place cannot deal effectively with the realities of today. Changes in economics, technology and populations are creating a set of challenges for older cultures, which these older cultures are unfit to manage. Seemingly we are being plunged headlong toward a crisis necessary to resolve the cultural inadequacies. The problem is that the crisis will be an immensely painful and horrible circumstance. We may simply have no choice, but to go through it, and hope we have the wisdom and strength to get to the other side of the abyss.

Crisis is Good. Crisis is a Messenger

― Bryant McGill

A crisis is a terrible thing to waste.

― Paul Romer

What can be done about undoing these toxic cultures without crisis? The usual remedy for a toxic culture is a crisis that demands effective action. This is an unpleasant prospect whether part of an organization or country, but it is the course we find ourselves on. One of the biggest problems with the toxic culture issue is its self-defeating nature. The toxic culture itself defends itself. Our politicians and managers are creatures whose success has been predicated on the toxic culture. These people are almost completely incapable of making the necessary decisions for avoiding the sorts of disasters that characterize a crisis. The toxic culture and those who succeed in them are unfit to resolve crises successfully. Our leaders are the most successful people in the toxic culture and act to defend such cultures in the face of overwhelming evidence that the culture is toxic. As such they do nothing to avoid the crisis even when it is obvious and make the eventual disaster inevitable.

Can we avoid this? I hope so, but I seriously doubt it. I fear that events will eventually unfold that will having us longing for the crisis to rescue us from the slow-motion zombie existence today’s current public-workplace cultures inflict on all of us.

The Chinese use two brush strokes to write the word ‘crisis.’ One brush stroke stands for danger; the other for opportunity. In a crisis, be aware of the danger–but recognize the opportunity.

― John F. Kennedy

We are ignoring the greatest needs & opportunities for improving computational science

We are lost, but we’re making good time.

― Star Trek V

Lately I’ve been doing a lot of thinking about the focus of research. Time and time again the entirety of our current focus seems to be driven by things that are not optimal. Little active or critical though has been applied to examining the best path forward. If progress is to be made a couple of questions should be central to our choices: is there a distinct opportunity to progress? Or would progress produce a large impact? Good choices would combine the opportunity for successful progress with impact and importance of the work. This simple principle in decision-making would make a huge difference at improving our choices.

The significant problems we face cannot be solved at the same level of thinking we were at when we created them.

– Albert Einstein

Examples of the two properties of opportunity and impact coming together abound in the history of science. The archetype of this would be the atomic bomb coming from the discoveries of basic scientific principles combined with overwhelming need in the socio-political worlds. At the end of the 19th century and beginning of the 20th century a massive revolution occurred in physics fundamentally changing our knowledge of the universe. The needs of global conflict pushed us to harness this knowledge to unleash the power of the atom. Ultimately the technology of atomic energy became a transformative political force probably stabilizing the world against massive conflict. More recently, computer technology has seen a similar set of events play out in a transformative way first scientifically, then in engineering and finally in profound societal impact we are just beginning to see unfold.

If we pull our focus into the ability of computational power to transform science, we can easily see the failure to recognize these elements in current ideas. We remain utterly tied to the pursuit of Moore’s law even as it lies in the morgue. Rather than examine the needs of progress, we remain tied to the route taken in the past. The focus of work has become ever more computer (machine) directed, and other more important and beneficial activities have withered from lack of attention. In the past I’ve pointed out the greater importance of modeling, methods, and algorithms in comparison to machines. Today we can look at another angle on this, the time it takes to produce useful computational results, or workflow.

Simultaneous to this unhealthy obsession, we ignore far great opportunities for progress sitting right in front of us. The most time consuming part of computational studies is rarely the execution of the computer code. The time consuming part of the solution to a problem is defining the model to be solved (often generating meshes), and analyzing the results from any solution. If one actually wishes to engage in rigorous V&V because the quality of the results really mattered, the focus would be dramatically different (working off the observation that V&V instills diminishing returns for speeding up computations). If one takes the view that V&V is simply the scientific method, the time demands only increase and dramatically and the gravity of engaging in time consuming activities only grows. What we suffer from is magical thinking on the part of those who “lead” computational science, by ignoring what should be done in favor of what can be more easily funded. This is not leadership, but rather the complete abdication of it.

When we look at the issue we are reminded of Amdahl’s law. Amdahl’s law basically establishes a law of has a program dominated by a single process eventually the parts you can’t speed up will eventually control the speed under optimization. Today we focus on speeding up the computation that isn’t even the dominant cost in computational science. We are putting almost no effort into speeding up the parts of computational science that take all the time. As a result the efforts put into improving computation will yield fleeting benefits to the actual conduct of science. This is a tragedy of lostopportunity. There is a common lack of appreciation for actual utility in research that arises from the naïve and simplistic view of how computational science is done. This view arises from the marketing of high performance computing work as basically only requiring a single magical calculation where science almost erupts spontaneously. Of course this never happens and the lack of scientific process in computational science is a pox on the field.

For engineering calculations with complex geometries, the time to develop a model often takes months. In many cases this time budget is dominated by mesh generation. There are aspects of trial and error where putative meshes are defined, tested and then refined. On top of this, the specification of the physical modeling of the problem is immensely time-consuming. Testing and running a computational model more quickly can come in handy as can faster mesh generation, but the human element in these practices are usually the choke point. We see precious little effort to do anything consequential to impact this part of the effort in computational science. For many problems this is the single largest component of the effort.

Once the model has been crafted and solved via computation, the results need to be analyzed and understood. Again, the human element in this practice is key. Effort in computing today for this purpose is concentrated in visualization technology. This may be the simplest and clearest example of the overwhelmingly transparent superficiality of current research. Visualization is useful for marketing science, but produces stunningly little actual science or engineering. We are more interested in funding tools for marketing work than actually doing work. Tools for extracting useful engineering or scientific data from calculation usually languish. They have little “sex appeal” compared to flashy visualization, but carry all the impact on the results that matter. If one is really serious about V&V all of these issues are compounded dramatically. For doing hard-nosed V&V visualization has almost no value whatsoever.

If you are inefficient, you have a right to be afraid of the consequences.

― Murad S. Shah

In the end all of this is evidence that current high performance computing programs have little interest in actual science or engineering. They are hardware focused because the people leading them like hardware; don’t care or understand science and engineering. The people running the show are little more than hardware-obsessed “fan boys” who care little about science. They succeed because of a track record of selling hardware-focused programs, not because it is the right thing to do. The role of computation is science should be central to our endeavor instead of a sideshow that receives little attention and less funding. Real leadership would provide a strong focus on completing important work that could impact the bottom line, doing better science with computational tools.

He who is not satisfied with a little, is satisfied with nothing.

― Epicurus

Dissipation isn’t bad or optional

Von Neumann told Shannon to call his measure entropy, since “no one knows what entropy is, so in a debate you will always have the advantage.

― Jeremy Campbell

Too often in seeing discourse about numerical methods, one gets the impression that dissipation is something to be avoided at all costs. Calculations are constantly under attack for being too dissipative. Rarely does one ever hear about calculations that are not dissipative enough. A reason for this is the tendency for too little dissipation to cause outright instability contrasted with too much dissipation with low-order methods. In between too little dissipation and instability are a wealth of unphysical solutions, oscillations and terrible computational results. These results may be all too common because of people’s standard disposition toward dissipation. The problem is that too few among the computational cognoscenti recognize that too little dissipation is as poisonous to results as too much (maybe more).

Why might I say that it is more problematic than too much dissipation? A big part of the reason is the nature physical realizability of solutions. A solution with too much dissipation is utterly physical in the sense that it can be found in nature. The solutions with too little dissipation more often than not are not found in nature. This is not because those solutions are unstable, but rather solutions that are stable, and have some dissipation; however, they simply aren’t dissipative enough to match natural law. What many do not recognize is that natural systems actually produce a large amount of dissipation without regard to the size of the mechanisms for explicit dissipative physics. This is both a profound physical truth, and the result of acute nonlinear focusing. It is important for numerical methods to recognize this necessity. Furthermore, this fact of nature reflects an uncomfortable coming together of modelling and numerical methods that many simply choose to ignore as an unpleasant reality.

In this house, we obey the laws of thermodynamics!

– Homer Simpson

Entropy stability is an increasingly important concept in the design of robust, accurate and convergent methods for solving systems defined by nonlinear conservation laws (see Tadmor 2016) The schemes are designed to automatically satisfy an entropy inequality that comes from the second law of thermodynamics, $d S/d t \le 0$. Implicit in the thinking about the satisfaction of the entropy inequality is a view that approaching the limit of $latex d S / d t = 0$ as viscosity becomes negligible (i.e., inviscid) is desirable. This is a grave error in thinking about the physical laws of direct interest, as the solution of conservation laws does not satisfy this limit when flows are inviscid. Instead the solutions of interest (i.e., weak solutions with discontinuities) in the inviscid limit approach a solution where the entropy production is proportional to variation in the large scale solution cubed, $d S / d t \le C \left(\Delta u\right)^3$. This scaling appears over and over in the solution of conservation laws including Burgers’ equation, the equations of compressible flow, MHD, and incompressible turbulence (Margolin & Rider, 2001). The seeming universality of these relations and their implications for numerical methods are discussed below in more detail, but follow the profound implications turbulence modelling are explored in detail for implicit LES modelling (our book edited by Grinstein, Margolin & Rider, 2007). Valid solutions will invariably produce the inequality, but the route to achievement varies greatly.

The satisfaction of the entropy inequality can be achieved in a number of ways and the one most worth avoiding is oscillations in the solution. Oscillatory solutions from nonlinear conservation laws are as common as they are problematic. In a sense, the proper solution is strong attractor for solutions and solutions will adjust to produce the necessary amount of dissipation in the solution. One vehicle for entropy production is oscillations in the solution field. Such oscillations are unphysical and can result in a host of issues undermining other physical aspects of the solution such as positivity of quantities such as density and pressure. They are to be avoided to whatever degree possible. If explicit action isn’t taken to avoid oscillations, one should expect them to appear.

There ain’t no such thing as a free lunch.

― Pierre Dos Utt

A more proactive approach to dissipation leading to entropy satisfaction is generally desirable. Another path toward entropy satisfaction is offered by numerical methods in control volume form. For second-order numerical methods the analysis of the approximation via the modified equation methodology unveils nonlinear dissipation terms that provide the necessary form for satisfying the entropy inequality via a nonlinearly dissipative term in the truncation error. This truncation error takes the form $C u_x u_{xx}$, which integrates to replicate inviscid dissipation as a residual term in the “energy” equation, $C\left(u_x\right)^3$. This term comes directly from being in conservation form and disappears when the approximation is in non-conservative from. In large part the overly large success of these second-order methods is related to this character.

Other options to add this character to solutions may be achieved by an explicit nonlinear (artificial) viscosity or through a Riemann solver. The nonlinear hyperviscosities discussed before on this blog work well. One of the pathological misnomers in the community is the belief that the specific form of the viscosity matters. This thinking infests direct numerical simulation (DNS) as it perhaps should, but the reality is that the form of dissipation is largely immaterial to establishing physically relevant flows. In other words inertial range physics does not depend upon the actual form or value of viscosity its impact is limited to the small scales of the flow. Each approach has distinct benefits as well as shortcomings. The key thing to recognize is the necessity of taking some sort of conscious action to achieve this end. The benefits and pitfalls of different approaches are discussed and recommended actions are suggested.

Enforcing the proper sort of entropy production through Riemann solvers is another possibility. A Riemann solver is simply a way of upwinding for a system of equations. For linear interaction modes the upwinding is purely a function of the characteristic motion in the flow, and induces a simple linear dissipative effect. This shows up as a linear even-order truncation error in modified equation analysis where the dissipation coefficient is proportional to the absolute value of the characteristic speed. For nonlinear modes in the flow, the characteristic speed is a function of the solution, which induces a set of entropy considerations. The simplest and most elegant condition is due to Lax, which says that the characteristics dictate that information flows into a shock. In a Lagrangian frame of reference for a right running shock this would look like, $c_{\mbox{left}} > c_{\mbox{shock}} > c_{\mbox{right}}$ with $c$ being the sound speed. It has a less clear, but equivalent form through a nonlinear sound speed, $c(\rho) = c(\rho_0) + \frac{\Delta \rho}{\rho} \frac{\partial \rho c}{\partial \rho}$. The differential term describes the fundamental derivative, which describes the nonlinear response of the sound speed to the solution itself. This same condition can be seen in a differential form and dictates some essential sign conventions in flows. The key is that these conditions have a degree of equivalence. The beauty is that the differential form lacks the simplicity of Lax’s condition, but establishes a clear connection to artificial viscosity.

The key to this entire discussion is realizing that dissipation is a fact of reality. Avoiding it is simply a demonstration of an inability to confront the non-ideal nature of the universe. This is simply contrary to progress and a sign of immaturity. Let’s just deal with reality.

The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

– Sir Arthur Stanley Eddington

References

Tadmor, E. (2016). Entropy stable schemes. Handbook of Numerical Analysis.

Margolin, L. G., & Rider, W. J. (2002). A rationale for implicit turbulence modelling. International Journal for Numerical Methods in Fluids, 39(9), 821-841.

Grinstein, F. F., Margolin, L. G., & Rider, W. J. (Eds.). (2007). Implicit large eddy simulation: computing turbulent fluid dynamics. Cambridge university press.

Lax, Peter D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Vol. 11. SIAM, 1973.

Harten, Amiram, James M. Hyman, Peter D. Lax, and Barbara Keyfitz. “On finite‐difference approximations and entropy conditions for shocks.” Communications on pure and applied mathematics 29, no. 3 (1976): 297-322.

Dukowicz, John K. “A general, non-iterative Riemann solver for Godunov’s method.” Journal of Computational Physics 61, no. 1 (1985): 119-137.