The road to Hell is paved with the best of conscious intentions.
― Elizabeth F. Howell
Let me get to one of the key punch lines for this post, “no amount of mesh refinement, accuracy or computer speed can rescue an incorrect model.” The entire reason for doing modeling and simulation is impacting our understanding or response to the reality of the Universe. The only fix for a bad model is a better model. Better models are not something we are investing much effort in. This gets to a fundamental imbalance in high performance computing where progress is now expected to come almost purely through improvements in the performance of hardware.
Success doesn’t come to you; you go to it.
― T. Scott McLeod
If the field were functioning in a healthy manner, the dynamic would be fluid and flexible. Sometimes a new model would spur developments in methods, algorithms for its solution. This would ultimately spill down to software and hardware developments. The dynamic that is working today would also manifest itself in the need for improvements in software and hardware to allow for solutions of meaningful models. The issue at hand today is the 20 year history of emphasis on hardware and its inability to yield progress as promised. It is time to recognize that the current trajectory is imbalanced and needs significant alteration to achieve progress commensurate with what has been marketed to society at large.
There can be no ultimate statements science: there can be no statements in science which can not be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them.
― Karl Popper
Modeling and simulation has become an end unto itself and lost some of its connection to its real reason for being done. The reason we conduct modeling and simulation is to understand, explain or influence reality. All of science has the objective of both uncovering the truth of the Universe and allowing man to apply some measure of control to it. As most things become to those practicing an art, modeling and simulation is a deep field combining many disparate fields together toward its accomplishment. This depth allows practitioners to lose track of the real purpose, and focus on the conduct of science to exclusion of its application.
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
Why would any of this make a difference?
By losing sight of the reason for conducting an activity causes a loss of the capacity to best utilize the field to make a difference. Science has a method and its manner conduct is important to keep in mind. Computational science is a bridge between the reality of physics and engineering and the computers that enable it. The biggest issue is the loss of perspective on what really determines the quality of modeling and simulation. Our current trajectory is focused almost exclusively on the speed of the computer as the route to quality. We have lost the important perspective that no computer can save a lousy model. It just assures a more expensive, high fidelity wrong solution.
The quest for absolute certainty is an immature, if not infantile, trait of thinking.
― Herbert Feigl
The wrong solutions we are getting are not terrible, just limited. Science works properly when there is a creative tension between experiments and theory. Theory can be powered by computing allowing the solution of models impossible without it. Experiments must test these theories either by being utterly new, or employing better diagnostics. Without the experiment to test, confirm or deny, theory can rot from within essentially losing connection with reality. This fate is befalling our theories today by fiat. Our models are almost assumed to be correct and not subject to rigorous testing. More powerful computers are simply assumed to yield better answers. No impetus is present to refine or develop better models where all evidence points toward their utter necessity.
…if you’re doing an experiment, you should report everything that you think might make it invalid—not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you’ve eliminated by some other experiment, and how they worked—to make sure the other fellow can tell they have been eliminated.
― Richard P. Feynman
Applied mathematics is a closely related field where the same slippage from reality is present. Again the utility of applied mathematics is distinctly like that of computing; it is utterly predicated upon the model’s quality visa-vis reality. In the period from World War 2 until around 1990, applied mathematics eagerly brought order and rigor to modeling, simulation and related activities. It became an able and honored partner for the advance and practice of science. Then it changed. It began to desire a deeper sense of mathematical honor as pure mathematics had in its eyes. In doing so applied math turned away from being applied and toward being governed by mathematical qualities. The lack of balance has emptied applied math’s capacity to advance science. The same has happened with computing. We are all poorer for it.
Science is not about making predictions or performing experiments. Science is about explaining.
― Bill Gaede
All of this may be overcome and the balance may be resurrected. All that is needed is to reconnect these fields with application. Application is a Gordian knot whose very nature powers science. Without the riddle and difficulty of application, the fields lose their vigor. The vigor is powered by attempting the solution of seemingly intractable problems. Without the continual injection of new ideas, the science cannot prosper. Such prosperity is currently being denied by a lack of connectivity to the very reality the fields discussed here could help to master. Such mastery is being denied by the lack of faith in our ability to take risks.
The intention (of an artist) is (the same as a scientist)…to discover and reveal what is unsuspected but significant in life.
― H W Leggett
Bad models abound in use today. A lot of them should be modified and discarded, but in today’s direction for scientific computing, we are simply claiming that a faster computer will open the door to solution. Many idealized equation sets are used in modeling that yield intrinsically unphysical solutions. The Euler equations without dissipation are a prime example. Plasma physics is yet another place where unphysical models are used because dissipation mechanisms are small. In macroscopic models dissipation is omnipresent, and leads to satisfaction of the second law of thermodynamic. Ideal equations remove this essential aspect of modeling by fiat.
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
In no place is this more greatly overloaded with context than turbulence. There is a misbegotten belief that solving the incompressible Navier-Stokes equations will unveil the secrets of turbulence. Incompressibility is fundamentally unphysical and may remove fundamental aspects of turbulence through its invocation. Incompressibility implies infinite speed of sound and a lack of thermodynamics. Connections between the incompressible and compressible equations only exist for adiabatic (dissipation-free) flows. Turbulence is characterized by dissipation in the absence of finite viscosity, which implies derivative singularities in the flow. Compressible fluids have this character and its nature is highly associated with the details of thermodynamics. Incompressible flows have not been clearly associated with this character, and the lack of thermodynamic is a likely source of this failing.
The plural of anecdote is not data.
― Marc Bekoff
Another aspect of our continuum modeling codes is the manner of describing material response. We tend to describe materials in a homogeneous manner that is we “paint” them into a physical region of the problem. All the aluminum in a problem will be described by the same constitutive laws without regard to the separation of scales between the computational mesh, and the physical scales in the material. This approach has been around for over 50 years and shows no signs of changing. It is actually long since past the time when this should have changed.
It is more Important to be of pure intention than of perfect action.
― Ilyas Kassam
The key is to apply the scientific method with rigor and vigor. Right now scientific computing has vacated its responsibility to apply the scientific method appropriately. Too often modeling and simulation are touted as being the third leg of science equal to theory and experiment. Modeling should always be beholding to experimental and field observation, and should the model be found to be in opposition to the observation, it must be found faulty. Modeling is rather an approach to more generally and broadly find solutions to theory. Thus theory can be extended to more nonlinear and complex models of reality. This should aid the ability of theory to describe the physical universe. Often simulation can act as a Laboratory for theory where suppositional theory can be tested for congruence with observation (computational astrophysics is a prime example of this).
Intention is one of the most powerful forces there is. What you mean when you do a thing will always determine the outcome. The law creates the world.
― Brenna Yovanoff
The bottom line is whether we are presently on a path that allows modeling and simulation to take its proper place in impacting reality, or explaining reality as part of the scientific method? I think the answer today is a clear and unequivocal, no. A combination of modern day political correctness regarding the power of computational hardware, over-selling of computing, fear and risk avoidance all lead to this. Each of these factors needs to be overcome to place us on the road to progress.
The tiniest of actions is always better than the boldest of intentions
― Robin Sharma
What needs to happen to make things better?
- Always connect the work in modeling and simulation to something the real world,
- Balance effort with the benefit of the world to the real world
- Find a way to give up on determinism to an appropriate degree, model the degree of variability seen in reality,
- Do not over emphasize the capacity of computational power to simply solve problems by fiat,
- Take risks especially risks that have a high chance for failure, but large payoffs,
- Allow glorious failure and reward risk-taking if done in a technically appropriate manner,
- New methods and algorithms provide potential for quantum improvements in efficiency and accuracy as well as the promise of new uses for computational models,
- No single aspect of modeling and simulation should be starved of attention as every part of this ecosystem must be healthy to achieve progress in predictive science,
- Stop settling for legacy models, methods and codes just because they are “good” enough focus on quality and excellence.
In the republic of mediocrity, genius is dangerous.
― Robert G. Ingersoll