Physics-Driven Regularization of Deep Neural Networks for Enhanced Engineering Design and Analysis
This addresses the challenge of enhancing prediction accuracy and interpretability in engineering systems where physical laws are available but often neglected, though it is incremental as it builds on existing regularization techniques.
The paper tackles the problem of improving deep neural networks for engineering design by incorporating known physical laws as regularization, resulting in models with smaller generalization errors and better interpretability compared to common regularization methods.
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.