Enforcing Analytic Constraints in Neural-Networks Emulating Physical Systems

TL;DR

This paper presents a systematic method to incorporate nonlinear analytic constraints into neural networks, ensuring physically consistent results in emulating physical systems like climate models without sacrificing accuracy.

Contribution

It introduces architectural and loss-based constraint enforcement techniques to neural networks, improving physical consistency and accuracy in modeling complex systems.

Findings

Conservation laws are enforced to machine precision.

Constraint enforcement reduces output errors in critical subsets.

Method maintains high performance while ensuring physical consistency.

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.