Enforcing Analytic Constraints in Neural-Networks Emulating Physical Systems

3 Sep 2019  ·  Tom Beucler, Michael Pritchard, Stephan Rasp, Jordan Ott, Pierre Baldi, Pierre Gentine ·

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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