Deep neural network enabled corrective source term approach to hybrid analysis and modeling

Hybrid Analysis and Modeling (HAM) is an emerging modeling paradigm which aims to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. Here, we introduce, justify and demonstrate a novel approach to HAM -- the Corrective Source Term Approach (CoSTA) -- which augments the governing equation of a PBM model with a corrective source term generated by a deep neural network (DNN). In a series of numerical experiments on one-dimensional heat diffusion, CoSTA is generally found to outperform comparable DDM and PBM models in terms of accuracy -- often reducing predictive errors by several orders of magnitude -- while also generalizing better than pure DDM. Due to its flexible but solid theoretical foundation, CoSTA provides a modular framework for leveraging novel developments within both PBM and DDM, and due to the interpretability of the DNN-generated source term within the PBM paradigm, CoSTA can be a potential door-opener for data-driven techniques to enter high-stakes applications previously reserved for pure PBM.