The first principle is that you must not fool yourself — and you are the easiest person to fool.
― Richard Feynmann
As computing becomes more and more important in science and engineering their credibility becomes essential. We are increasingly relying upon modeling and simulation to provide key input to a variety of endeavors many of which are high consequence. A good question to ask is why should I believe a computation? Why should I trust it? Why do I believe it? Do I know where the calculation breaks down? Do I understand the errors that are incurred in simulation? What could go wrong and what has been done to minimize that possibility?
Belief can be manipulated. Only knowledge is dangerous.
This is where the entire practice of verification and validation comes in. The entirety of what V&V does (or should do) is developing an evidentiary basis for answering the above questions in an affirmative manner. Doing V&V is a way of establishing the credibility of a calculation or calculational capability. A key is the lack of definitive proof in computations; you only build the case that the computation is credible. In a deep sense V&V is the due diligence aspect of computing and as due diligence it is both incredibly important and terribly unsexy.
― Richard Feynmann
Once the basic credibility has been established using V&V one can start to work toward enhancing this state. A key aspect of V&V regards a two-sided relationship for credibility. Often it is the positive credibility affirming aspect where the correctness of a computation is demonstrated which is thought of. The flip side of the picture is the negative aspects of V&V. These are equally important where V&V finds the limits of computational capability. In this sense the bounds of knowledge and capability are mapped through V&V. This defines useful and important work that can expand the capability toward new vistas.
All along the path toward increased credibility whenever you are doing useful work with computation uncertainty should be quantified. This experience should be the stock and trade with every verification and validation exercise. Often it is not. With verification, the error should be estimated, and the order of accuracy quantified. Far too often it is not conducted. The usual credibility is the establishment of mesh sensitivity, which is dangerous because it often gives a false or wrong sense of confidence. Uncertainty quantification should always accompany the validation exercise so that the simulated results can be compared directly with the experimental including the uncertainty.
The easier it is to quantify, the less it’s worth.
— Seth Godin
All of these provide a leveling of the credibility of the simulation for the intended use. In addition to providing the credibility basis, the V&V with associated UQ provides the methodology for defining details of any use of computation in a serious manner.
Doubt is an uncomfortable condition, but certainty is a ridiculous one.