Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach

TL;DR

This paper introduces a hybrid modeling approach combining physics-based equations with data-driven neural networks to improve accuracy, interpretability, and generalizability in safety-critical systems like heat diffusion.

Contribution

It presents a novel corrective source term approach that integrates physics-based models with neural networks, demonstrating superior performance over traditional methods.

Findings

Outperforms pure physics-based and data-driven models in accuracy

Enhances model generalizability to unseen scenarios

Provides interpretability of the neural network component

Abstract

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately, the two most commonly used modeling approaches, physics-based modeling (PBM) and data-driven modeling (DDM) fail to satisfy all these requirements. In the current work, we demonstrate how a hybrid approach combining the best of PBM and DDM can result in models which can outperform them both. We do so by combining partial differential equations based on first principles describing partially known physics with a black box DDM, in this case, a deep neural network model compensating for the unknown physics. First, we present a mathematical argument for why this approach should work and then apply the hybrid approach to model two dimensional heat diffusion problem with an unknown source term. The result demonstrates the method's superior performance in terms of accuracy, and generalizability. Additionally, it is shown how the DDM part can be interpreted within the hybrid framework to make the overall approach reliable.