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

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety–critical applications require accurate, interpretable, computationally efficient, generalizable models. Unfortunately, the two most commonly used modeling approaches, physics-based (PBM) data-driven (DDM) struggle to satisfy all these requirements. In current work, we demonstrate how a hybrid approach combining best of PBM DDM can result in models that outperform both them. We do so by partial differential equations based on first principles describing partially known physics with black box DDM, this case, deep neural network model compensating for unknown physics. The novelty work is theoretical contribution presenting sound mathematical argument why should work. backed an array experiments two-dimensional heat diffusion problem source terms. demonstrates method’s superior performance accuracy generalizability. Additionally, it shown part be interpreted within framework make overall reliable. approach, as see, will door opener underutilized DDMs high stake applications.