Jointly learning variational data assimilation models and solvers for geophysical dynamics

Abstract

This paper addresses representation learning for the resolution of inverse problems with geophysical dynamics. Among others, examples of inverse problems of interest include space-time interpolation, short-term forecasting, conditional simulation w.r.t. available observations, downscaling problems... From a methodological point of view, we rely on a variational data assimilation framework. Data assimilation (DA) aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Here, we investigate DA from a machine learning point of view backed by an underlying variational representation. Using automatic differentiation tools embedded in deep learning frameworks, we introduce endto-end neural network architectures for variational data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the neural networks models using both supervised and unsupervised strategies. We first illustrate applications to the reconstruction of Lorenz-63 and Lorenz-96 systems from partial and noisy observations. Whereas the gain issued from the supervised learning setting emphasizes the relevance of groundtruthed observation dataset for real-world case-studies, these results also suggest new means to design data assimilation models from data. Especially, they suggest that learning task-oriented representations of the underlying dynamics may be beneficial. We further discuss applications to short-term forecasting and sampling design along with preliminary results for the reconstruction of sea surface currents from satellite altimetry data.