Our Philosophy

Predicting the behavior of the physical world is central to both science and engineering. Advances in computer simulations, considered as a new tool of science and engineering along with theory and experiment, have lead researchers to contemplate predictions of increasingly more complicated physical phenomena. However, the complexity of recent simulations makes their reliability difficult to assess and one faces the danger of drawing false conclusions from inaccurate predictions.

The Center for Predictive Engineering and Computational Sciences (PECOS) is dedicated to the development of methods and techniques for reliable computational predictions through the verification of numerical computations, the validation of the underlying physical models and quantification of the uncertainties in the predictions.

Verification of numerical computations, in which one asks if numerical results are an accurate representation of the solution to the mathematical model that is being solved, is relatively well understood. It requires careful attention to good software engineering practices, continuous software testing, and control of numerical discretization errors, through error estimation and adaptivity. While verification processes are well understood, they require substantial effort. Because verification of numerical results is a prerequisite for reliable computational predictions, verification processes are integral to all activities in the PECOS center.

Validation of physical models and the quantification of uncertainty in predictions are not well established. They are also closely related to each other and to the calibration of uncertain model parameters. At the PECOS center, development of techniques for calibration, validation and uncertainty quantification, are guided by the following principles:

1. Reliable experimental data with rigorous uncertainties is necessary for calibration, validation and uncertainty quantification. This requires verification and validation of the experimental measurements and the subsequent data reduction models.
2. Calibration and validation in the presence of uncertainty are statistical, and posed in the context of the Bayesian interpretation of probability and Bayesian inference. Thus, our prior knowledge (or lack thereof) of the model parameters, our uncertainty in the structure of the mathematical model, and the uncertainty inherent in experimental data are all expressed in terms of probability distributions.
3. As argued by Karl Popper, mathematical models cannot be determined to be valid, they can only be invalidated by experimental observations. Thus the validation process is one of gaining increasing confidence in a model as repeated attempts to invalidate it by experimental observations fails.
4. (in)Validation is done in the context of a specified prediction, and the purpose for which it is being performed. In particular, the (in)validity of a model is assessed in the context of a quantity to be predicted (the Quantity of Interest, or QoI), and the requirements for the decision to be made based on the prediction. The reason is that a model can be valid for some predictions, but not others.
5. For complex multi-physics systems and models, the calibration and validation process is hierarchical. In such systems, validation is pursued for the simplest possible component models first, and then for increasingly complex combination of coupled models. This is necessary because multi-physics coupling will commonly involve new “coupling” models that need calibration and validation, and because component models may themselves be invalid under the conditions present in the coupled system.
6. Calibration and validation are iterative processes: in case a model is considered invalid, proper action, for example, requiring more or better calibration data or using a new mathematical model, are pursued to correct the failure.