Neural Koopman prior for data assimilation

TL;DR

This paper introduces a neural network model based on Koopman operator theory that embeds dynamical systems in latent spaces for improved long-term data reconstruction and assimilation, especially with irregularly-sampled data.

Contribution

It presents a novel neural Koopman-based architecture that enables long-term reconstruction and data assimilation, leveraging physical priors and supporting self-supervised learning.

Findings

Effective long-term reconstruction of irregular time series.

Successful use as a prior in variational data assimilation.

Promising applications in time series interpolation and forecasting.

Abstract

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.