Data-driven algorithms, in particular neural networks, can emulate the effect of unresolved processes in coarse-resolution climate models if trained on high-resolution simulation data. However, they may violate key physical constraints and make large errors when evaluated outside of their training set. I will share progress towards overcoming these two challenges in the case of machine learning the effect of subgrid-scale convection and clouds on the large-scale climate. First, physical constraints can be enforced in neural networks, either approximately by adapting the loss function or to within machine precision by adapting the architecture. Second, as these physical constraints are insufficient to guarantee generalizability, I additionally propose to physically rescale the inputs and outputs of machine learning algorithms to help them generalize to unseen climates. Overall, these results suggest that explicitly incorporating physical knowledge into data-driven models of climate processes may improve their consistency, stability, and ability to generalize across climate regimes.

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