Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Author(s)
Arbabi, Hassan
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The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential operators requires extensive spatiotemporal data. For learning coarse-scale PDEs from computational fine-scale simulation data, the training data collection process can be prohibitively expensive. We propose to transformatively facilitate this training data collection process by linking machine learning (here, neural networks) with modern multiscale scientific computation (here, equation-free numerics). These equation-free techniques operate over sparse collections of small, appropriately coupled, space-time subdomains (“patches”), parsimoniously producing the required macro-scale training data. Our illustrative example involves the discovery of effective homogenized equations in one and two dimensions, for problems with fine-scale material property variations. The approach holds promise towards making the discovery of accurate, macro-scale effective materials PDE models possible by efficiently summarizing the physics embodied in “the best” fine-scale simulation models available.
Date issued
2020-10-29Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
JOM
Publisher
Springer US
Citation
Arbab, Hassan et al. “Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations.” JOM, 72 (October 2020): 4444–4457 © 2020 The Author(s)
Version: Author's final manuscript
ISSN
0098-4558