Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach
This work addresses the need for reliable hybrid models in safety-critical technologies like digital twins and autonomous systems, though it appears incremental as it builds on existing hybrid approaches.
The authors tackled the challenge of creating accurate, interpretable, and generalizable models for safety-critical applications by combining physics-based modeling with data-driven deep neural networks to compensate for unknown physics. They demonstrated superior performance in modeling a 2D heat diffusion problem with an unknown source term, achieving improved accuracy and generalizability.
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.