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Enforcing Analytic Constraints in Neural Networks Emulating Physical Systems

Tom Beucler, Michael Pritchard, Stephan Rasp, Jordan Ott, Pierre Baldi, and Pierre Gentine
Phys. Rev. Lett. 126, 098302 – Published 4 March 2021
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Abstract

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to convective processes for climate modeling, architectural constraints enforce conservation laws to within machine precision without degrading performance. Enforcing constraints also reduces errors in the subsets of the outputs most impacted by the constraints.

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  • Received 17 September 2019
  • Revised 9 November 2020
  • Accepted 1 February 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.098302

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsNonlinear DynamicsInterdisciplinary PhysicsNetworks

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Teaching a Neural Network the Hard Way

Published 4 March 2021

A neural network can be made to produce more reliable predictions of nonlinear systems if it is created with conservation laws built in.

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Authors & Affiliations

Tom Beucler1,2,*, Michael Pritchard1, Stephan Rasp3, Jordan Ott4, Pierre Baldi4, and Pierre Gentine2

  • 1Department of Earth System Science, University of California, Irvine, California 92697-3100, USA
  • 2Department of Earth and Environmental Engineering, Columbia University, New York, New York 10027, USA
  • 3Technical University of Munich, Boltzmannstr. 3 85748 Garching, Munich, Germany
  • 4Department of Computer Science, University of California, Irvine, California 92697, USA

  • *tom.beucler@gmail.com

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Issue

Vol. 126, Iss. 9 — 5 March 2021

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