Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
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11837_2020_4399_ReferencePDF.pdf
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3.35 MB
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Author(s)
Arbabi, Hassan
Date Issued
October 29, 2020
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s11837-020-04399-8
