Verification of Data-Driven Models of Physical Phenomena using Interpretable Approximation

Abstract

Machine-learned models, specifically neural networks, are increasingly used as “closures” or “constitutive models” in engineering simulators to represent fine-scale physical phenomena that are too computationally expensive to resolve explicitly. However, these neural net models of unresolved physical phenomena tend to fail unpredictably and are therefore not used in mission-critical simulations. In this report, we describe new methods to authenticate them, i.e., to determine the (physical) information content of their training datasets, qualify the scenarios where they may be used and to verify that the neural net, as trained, adhere to physics theory. We demonstrate these methods with neural net closure of turbulent phenomena used in Reynolds Averaged Navier-Stokes equations. We show the types of turbulent physics extant in our training datasets, and, using a test flow of an impinging jet, identify the exact locations where the neural network would be extrapolating i.e., where it would be used outside the feature-space where it was trained. Using Generalized Linear Mixed Models, we also generate explanations of the neural net (à la Local Interpretable Model agnostic Explanations) at prototypes placed in the training data and compare them with approximate analytical models from turbulence theory. Finally, we verify our findings by reproducing them using two different methods.