Abstract
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.
Highlights
The recent wave of digitalization has given a push to emerging technologies like digital twins
To quantify the models’ performance, we present the temporal development of the relative l2-errors, Tpn − Trnef 2 / Trnef 2, Tdn − Trnef 2 / Trnef 2 and Thn − Trnef 2 / Trnef 2, of the physics-based modeling (PBM), data-driven modeling (DDM)- and Hybrid Analysis and Modeling (HAM) predictions with respect to the sampled manufactured solution Trnef
We present the temperature profiles predicted by PBM, DDM and HAM at the final time level n = Nt − 1 alongside the manufactured solution T (x, tNt−1; α)
Summary
The recent wave of digitalization has given a push to emerging technologies like digital twins. A digital twin is defined as a virtual representation of a physical asset enabled through data and simulators for real-time prediction, optimization, monitoring, controlling, and improved decision making (Rasheed et al, 2020). Paramount to digital twins’ success is the level of physical realism that can be instilled into them. In this regard, as noticed by Rasheed et al (2020), modeling plays an important role. A digital twin offers huge potential in many industries, adaptation of the digital twin technology has been stagnated since its inception, mainly due to the lack of methodological works. The role of surrogate models in the development of digital twin
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