Composing Partial Differential Equations with Physics-Aware Neural Networks

We introduce a compositional physics-aware FInite volume 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 mo...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Karlbauer, Matthias, Praditia, Timothy, Otte, Sebastian, Oladyshkin, Sergey, Nowak, Wolfgang, Butz, Martin V
Format: Article
Language:English
Subjects:
Artificial neural networks
Boundary conditions
Diffusion
Machine learning
Mathematical models
Model accuracy
Neural networks
Partial differential equations
Physics
Sorption
Two dimensional models
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce a compositional physics-aware FInite volume 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 (Burgers', 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.
ISSN:2331-8422