Enforcing Analytic Constraints in Neural-Networks Emulating Physical Systems. Beucler, T., Pritchard, M., Rasp, S., Gentine, P., Ott, J., & Baldi, P. *arXiv:1909.00912 [physics]*, September, 2019. arXiv: 1909.00912Paper abstract bibtex Neural networks can emulate non-linear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. In this letter, we introduce a systematic way of enforcing analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to the modeling of convective processes for climate modeling, architectural constraints can enforce conservation laws to within machine precision without degrading performance. Furthermore, enforcing constraints can reduce the error of variables closely related to the constraints.

@article{beucler_enforcing_2019,
title = {Enforcing {Analytic} {Constraints} in {Neural}-{Networks} {Emulating} {Physical} {Systems}},
url = {http://arxiv.org/abs/1909.00912},
abstract = {Neural networks can emulate non-linear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. In this letter, we introduce a systematic way of enforcing analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to the modeling of convective processes for climate modeling, architectural constraints can enforce conservation laws to within machine precision without degrading performance. Furthermore, enforcing constraints can reduce the error of variables closely related to the constraints.},
urldate = {2019-09-27},
journal = {arXiv:1909.00912 [physics]},
author = {Beucler, Tom and Pritchard, Michael and Rasp, Stephan and Gentine, Pierre and Ott, Jordan and Baldi, Pierre},
month = sep,
year = {2019},
note = {arXiv: 1909.00912},
keywords = {Physics - Atmospheric and Oceanic Physics, Physics - Computational Physics},
}

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