Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling
Tom Beucler, Stephan Rasp, Michael Pritchard, Pierre Gentine
TL;DR
The paper addresses the challenge of energy and mass conservation in neural-network emulators for cloud processes in climate models. It proposes and evaluates two conservation strategies—penalty-based constraint losses and architecture-based constraint layers—applied to a convective parametrization in an ocean-world climate model. Architecture-constrained networks enforce conservation to numerical precision and, along with a light penalty in the loss function, improve generalization to warming scenarios ($+4\,\mathrm{K}$) while preserving radiative-flux fidelity as evidenced by high $R^2$ on the outgoing longwave radiation field. The work offers a practical route to integrating physically constrained neural emulators into climate predictions, reducing biases from small forcings and enhancing extrapolation to climate-change conditions.
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.