Learning Variational Data Assimilation Models and Solvers

TL;DR

This paper introduces neural network architectures for variational data assimilation, enabling end-to-end training with supervised and unsupervised methods, leading to improved reconstruction performance on Lorenz systems.

Contribution

It presents a novel neural network-based framework for data assimilation, combining a variational model and solver, trained end-to-end using deep learning tools.

Findings

Significant improvement over classic gradient-based methods in Lorenz systems

End-to-end neural models can outperform models based on true ODE representations

Training with both supervised and unsupervised strategies enhances performance

Abstract

This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for 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 NN models using both supervised and unsupervised strategies. Our numerical experiments on Lorenz-63 and Lorenz-96 systems report significant gain w.r.t. a classic gradient-based minimization of the variational cost both in terms of reconstruction performance and optimization complexity. Intriguingly, we also show that the variational models issued from the true Lorenz-63 and Lorenz-96 ODE representations may not lead to the best reconstruction performance. We believe these results may open new research avenues for the specification of assimilation models in geoscience.