Neural Koopman prior for data assimilation
This work addresses the problem of handling irregular time series data in dynamical systems for researchers and practitioners in fields like physics and engineering, representing an incremental improvement by integrating neural networks with established mathematical theory.
The paper tackles the challenge of modeling irregularly-sampled time series by introducing a neural network architecture based on Koopman operator theory, enabling long-term continuous reconstruction and demonstrating its use as a prior for variational data assimilation in tasks like interpolation and forecasting.
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.