Gradient-free online learning of subgrid-scale dynamics with neural emulators
This work addresses the challenge of learning parametrizations for climate models, which is incremental as it builds on online strategies but adapts them to non-differentiable solvers.
The authors tackled the problem of training machine learning-based subgrid parametrizations online for non-differentiable numerical solvers, using a neural emulator to enable gradient propagation without computing the solver's gradient, and applied it to chaotic systems like Lorenz-96 and a quasi-geostrophic system, achieving recovery of most online strategy benefits.
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.