Physics-Driven Regularization of Deep Neural Networks for Enhanced Engineering Design and Analysis

TL;DR

This paper presents a physics-driven regularization technique for deep neural networks that incorporates governing physical laws, improving interpretability and generalization in engineering prediction tasks.

Contribution

It introduces a novel regularization method that enforces physical law compliance in DNN training, enhancing model accuracy and interpretability in engineering applications.

Findings

Regularization improves model interpretability and reduces generalization error.

The method outperforms common regularization techniques in synthetic examples.

Superior accuracy demonstrated in real-world engineering problems.

Abstract

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in addition to training data, partial or complete information on a set of governing laws is also available. These laws often appear in the form of differential equations, derived from first principles, empirically-validated laws, or domain expertise, and are usually neglected in data-driven prediction of engineering systems. We propose a training approach that utilizes the known governing laws and regularizes data-driven DNN models by penalizing divergence from those laws. The first two numerical examples are synthetic examples, where we show that in constructing a DNN model that best fits the measurements from a physical system, the use of our proposed regularization results in DNNs that are more interpretable with smaller generalization errors, compared to other common regularization methods. The last two examples concern metamodeling for a random Burgers' system and for aerodynamic analysis of passenger vehicles, where we demonstrate that the proposed regularization provides superior generalization accuracy compared to other common alternatives.