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

Unlike the traditional subgrid scale parameterizations used in climate models, current neural network (NN) 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 NN parameterizations and calibrate them online. The calibration of the NN parameterization is achieved in two steps. First, some model parameters are included within the NN model input. This NN model is fitted at once for a range of values of the parameters, using an offline metric. Second, once the NN parameterization has been plugged into the climate model, the parameters included among the NN 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 climate model with NN based physics.