Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling

TL;DR

This paper introduces methods to enforce energy and mass conservation in neural network emulators for climate modeling, improving their physical fidelity and generalization to changing conditions.

Contribution

It proposes two novel approaches—loss function constraints and architectural constraints—to ensure conservation laws in neural network climate emulators.

Findings

Architecture constraints enforce conservation with high numerical precision.

All constraints improve generalization to conditions outside training data.

Conservation enforcement enhances long-term climate prediction accuracy.

Abstract

Artificial neural-networks have the potential to emulate cloud processes with higher accuracy than the semi-empirical emulators currently used in climate models. However, neural-network models do not intrinsically conserve energy and mass, which is an obstacle to using them for long-term climate predictions. Here, we propose two methods to enforce linear conservation laws in neural-network emulators of physical models: Constraining (1) the loss function or (2) the architecture of the network itself. Applied to the emulation of explicitly-resolved cloud processes in a prototype multi-scale climate model, we show that architecture constraints can enforce conservation laws to satisfactory numerical precision, while all constraints help the neural-network better generalize to conditions outside of its training set, such as global warming.