How to calibrate a climate model with neural network based physics?

Submitted to Geophysical Research Letters.

Unlike the traditional subgrid scale parameterizations used in climate models, current machine learning (ML) parameterizations are only tuned offline, by minimizing a loss function on outputs from high resolution models. This approach often leads to numerical instabilities and long-term biases. Here, we propose a method to design tunable ML parameterizations and calibrate them online. The calibration of the ML parameterization is achieved in two steps. First, some model parameters are included within the ML model input. This ML model is fitted at once for a range of values of the parameters, using an offline metric. Second, once the ML parameterization has been plugged into the climate model, the parameters included among the ML inputs are optimized with respect to an online metric quantifying errors on long-term statistics. We illustrate our method with two simple dynamical systems. Our approach significantly reduces long-term biases of the ML model.