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Type: Journal article
Title: Linking machine learning with multiscale numerics: data-driven discovery of homogenized equations
Author: Arbabi, H.
Bunder, J.E.
Samaey, G.
Roberts, A.J.
Kevrekidis, I.G.
Citation: Journal of Metals, 2020; 72(12):4444-4457
Publisher: Springer Nature
Issue Date: 2020
ISSN: 1047-4838
Statement of
Hassan Arbabi, Judith E. Bunder, Giovanni Samaey, Anthony J. Roberts, and Ioannis G. Kevrekidis
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.
Rights: © 2020 The Minerals, Metals & Materials Society
DOI: 10.1007/s11837-020-04399-8
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Mathematical Sciences publications

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