Composing Partial Differential Equations with Physics-Aware Neural Networks

• URL: http://arxiv.org/abs/2111.11798v1
• Date: Tue, 23 Nov 2021 11:27:13 GMT
• Title: Composing Partial Differential Equations with Physics-Aware Neural Networks
• Authors: Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, Wolfgang Nowak, and Martin V. Butz
• Abstract summary: We introduce a physics-aware neural network (FINN) for learning advection-diffusion processes. With only one tenth of the number of parameters on average, FINN outperforms machine learning and other state-of-the-art physics-aware models.
• Score: 0.831246680772592
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We introduce a compositional physics-aware neural network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the learning abilities of artificial neural networks with physical and structural knowledge from numerical simulation by modeling the constituents of partial differential equations (PDEs) in a compositional manner. Results on both one- and two-dimensional PDEs (Burger's, diffusion-sorption, diffusion-reaction, Allen-Cahn) demonstrate FINN's superior modeling accuracy and excellent out-of-distribution generalization ability beyond initial and boundary conditions. With only one tenth of the number of parameters on average, FINN outperforms pure machine learning and other state-of-the-art physics-aware models in all cases -- often even by multiple orders of magnitude. Moreover, FINN outperforms a calibrated physical model when approximating sparse real-world data in a diffusion-sorption scenario, confirming its generalization abilities and showing explanatory potential by revealing the unknown retardation factor of the observed process.

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