Enforcing Analytic Constraints in Neural Networks Emulating Physical Systems

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 2019Revised 9 November 2020Accepted 1 February 2021DOI:https://doi.org/10.1103/PhysRevLett.126.098302© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtmospheric fluid dynamicsAtmospheric scienceClimate researchConvectionGeophysical fluid dynamicsOptimization problemsStratified geophysical flowsThermodynamicsTurbulencePhysical SystemsArtificial neural networksNetworksInterdisciplinary PhysicsNonlinear DynamicsFluid Dynamics