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

Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling