Learning Variational Data Assimilation Models and Solvers

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.

References in corpus (6)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Data-driven discovery of coordinates and governing equations
• A Review of Convolutional Neural Networks for Inverse Problems in Imaging
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
• DeepISP: Towards Learning an End-to-End Image Processing Pipeline
• Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization

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