Composing Partial Differential Equations with Physics-Aware Neural NetworksDownload PDF


Sep 29, 2021 (edited Nov 19, 2021)ICLR 2022 Conference Blind SubmissionReaders: Everyone
  • Keywords: physics-aware neural networks, partial differential equations, advection-diffusion equations, learning constituents, out-of-distribution generalization
  • 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) demonstrate FINN's superior process 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.
  • One-sentence Summary: A physics-aware neural network for compositional learning of constituents of partial differential equations demonstrating eminent generalization abilities.
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