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

• Published in: Neural networks Vol. 146; no. C; pp. 181 - 199
• Main Authors: Blakseth, Sindre Stenen, Rasheed, Adil, Kvamsdal, Trond, San, Omer
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.02.2022; Elsevier
• Subjects: Corrective source term approach (CoSTA); Deep neural networks; Digital twins; Explainable AI; Hybrid analysis and modeling; Neural Networks, Computer; Physics; Physics-based modeling; Deep neural networks; Explainable AI; Hybrid analysis and modeling; Digital twins; Corrective source term approach (CoSTA); Physics-based modeling
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2021.11.021

In this work, we introduce, justify and demonstrate the Corrective Source Term Approach (CoSTA)—a novel approach to Hybrid Analysis and Modeling (HAM). The objective of HAM is to combine physics-based modeling (PBM) and data-driven modeling (DDM) to create generalizable, trustworthy, accurate, computationally efficient and self-evolving models. CoSTA achieves this objective by augmenting the governing equation of a PBM model with a corrective source term generated using a deep neural network. In a series of numerical experiments on one-dimensional heat diffusion, CoSTA is 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. Its theoretical foundation also ensures that CoSTA can be used to model any system governed by (deterministic) partial differential equations. Moreover, CoSTA facilitates interpretation of the DNN-generated source term within the context of PBM, which results in improved explainability of the DNN. These factors make CoSTA a potential door-opener for data-driven techniques to enter high-stakes applications previously reserved for pure PBM. •CoSTA combines differential equations and neural networks•CoSTA exploits the best of both the physics-based and data-driven models•CoSTA is applied to heat transfer problems with unknown/unmodeled physics•CoSTA outperforms both physics-based and data-driven models•CoSTA can unlock the full potential of neural networks in high-stakes applications