Learning Variational Data Assimilation Models and Solvers
This work addresses data assimilation problems in geoscience, offering a novel learning-based approach that could improve model specification, though it is incremental in applying deep learning tools to an existing framework.
The paper tackles variational data assimilation by introducing end-to-end neural network architectures for reconstructing state evolution from noisy, irregular observations, reporting significant gains in reconstruction performance and optimization complexity on Lorenz-63 and Lorenz-96 systems compared to classic gradient-based methods.
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.