Deep prior in variational assimilation to estimate an ocean circulation without explicit regularization

Abstract

Abstract Many applications in geosciences require solving inverse problems to estimate the state of a physical system. Data assimilation provides a strong framework to do so when the system is partially observed and its underlying dynamics are known to some extent. In the variational flavor, it can be seen as an optimal control problem where initial conditions are the control parameters. Such problems are often ill-posed, regularization may be needed using explicit prior knowledge to enforce a satisfying solution. In this work, we propose to use a deep prior, a neural architecture that generates potential solutions and acts as implicit regularization. The architecture is trained in a fully-unsupervised manner using the variational data assimilation cost so that gradients are backpropagated through the dynamical model and then through the neural network. To demonstrate its use, we set a twin experiment using a shallow-water toy model, where we test various variational assimilation algorithms on an ocean-like circulation estimation.