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.
- 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)
synopsis
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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