Using Conservation Laws to Infer Deep Learning Model Accuracy of Richtmyer-meshkov Instabilities

TL;DR

This paper explores using physical conservation laws to evaluate the accuracy of deep learning models predicting Richtmyer-Meshkov Instability formations, finding mass and momentum conservation as weak but useful indicators.

Contribution

The study introduces a method to infer deep learning model accuracy for RMI predictions using conservation laws, linking physical principles with model validation.

Findings

Deep learning models accurately predict RMI evolution across various conditions.

Conservation of mass and momentum weakly correlates with model accuracy.

Physical conservation laws can serve as quick, relative accuracy measures for predictions.

Abstract

Richtmyer-Meshkov Instability (RMI) is a complicated phenomenon that occurs when a shockwave passes through a perturbed interface. Over a thousand hydrodynamic simulations were performed to study the formation of RMI for a parameterized high velocity impact. Deep learning was used to learn the temporal mapping of initial geometric perturbations to the full-field hydrodynamic solutions of density and velocity. The continuity equation was used to include physical information into the loss function, however only resulted in very minor improvements at the cost of additional training complexity. Predictions from the deep learning model appear to accurately capture temporal RMI formations for a variety of geometric conditions within the domain. First principle physical laws were investigated to infer the accuracy of the model's predictive capability. While the continuity equation appeared to show no correlation with the accuracy of the model, conservation of mass and momentum were weakly correlated with accuracy. Since conservation laws can be quickly calculated from the deep learning model, they may be useful in applications where a relative accuracy measure is needed.