Guillaume Balarac

Hugo Frezat, Julien Le Sommer, Ronan Fablet et al.

The use of machine learning to build subgrid parametrizations for climate models is receiving growing attention. State-of-the-art strategies address the problem as a supervised learning task and optimize algorithms that predict subgrid fluxes based on information from coarse resolution models. In practice, training data are generated from higher resolution numerical simulations transformed in order to mimic coarse resolution simulations. By essence, these strategies optimize subgrid parametrizations to meet so-called $\textit{a priori}$ criteria. But the actual purpose of a subgrid parametrization is to obtain good performance in terms of $\textit{a posteriori}$ metrics which imply computing entire model trajectories. In this paper, we focus on the representation of energy backscatter in two dimensional quasi-geostrophic turbulence and compare parametrizations obtained with different learning strategies at fixed computational complexity. We show that strategies based on $\textit{a priori}$ criteria yield parametrizations that tend to be unstable in direct simulations and describe how subgrid parametrizations can alternatively be trained end-to-end in order to meet $\textit{a posteriori}$ criteria. We illustrate that end-to-end learning strategies yield parametrizations that outperform known empirical and data-driven schemes in terms of performance, stability and ability to apply to different flow configurations. These results support the relevance of differentiable programming paradigms for climate models in the future.

Hugo Frezat, Ronan Fablet, Guillaume Balarac et al.

In this paper, we propose a generic algorithm to train machine learning-based subgrid parametrizations online, i.e., with \textit{a posteriori} loss functions, but for non-differentiable numerical solvers. The proposed approach leverages a neural emulator to approximate the reduced state-space solver, which is then used to allow gradient propagation through temporal integration steps. We apply this methodology on a chaotic two-timescales Lorenz-96 system and a single layer quasi-geostrophic system with zonal dynamics, known to be highly unstable with offline strategies. Using our algorithm, we are able to train a parametrization that recovers most of the benefits of online strategies without having to compute the gradient of the original solver. We found that training the neural emulator and parametrization components separately with different loss quantities is necessary in order to minimize the propagation of approximation biases. Experiments on emulator architectures with different complexities also indicates that emulator performance is key in order to learn an accurate parametrization. This work is a step towards learning parametrization with online strategies for climate models.

Hugo Frezat, Julien Le Sommer, Ronan Fablet et al.

Modeling the subgrid-scale dynamics of reduced models is a long standing open problem that finds application in ocean, atmosphere and climate predictions where direct numerical simulation (DNS) is impossible. While neural networks (NNs) have already been applied to a range of three-dimensional flows with success, two dimensional flows are more challenging because of the backscatter of energy from small to large scales. We show that learning a model jointly with the dynamical solver and a meaningful \textit{a posteriori}-based loss function lead to stable and realistic simulations when applied to quasi-geostrophic turbulence.