Learning Optimal Filters Using Variational Inference

TL;DR

This paper introduces a variational inference framework to learn optimal filtering parameters and analysis maps, improving the accuracy of state estimation in complex dynamical systems like weather prediction.

Contribution

It presents a novel variational inference approach for learning analysis maps and filter parameters, enhancing filtering accuracy for nonlinear and high-dimensional systems.

Findings

Successfully learned gain matrices for linear and nonlinear systems

Optimized inflation and localization parameters for ensemble Kalman filters

Potential to develop new filtering algorithms with flexible analysis maps

Abstract

Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction. However, the filtering distribution is generally intractable to obtain for high-dimensional, nonlinear systems. Filters used in practice, such as the ensemble Kalman filter (EnKF), provide biased probabilistic estimates for nonlinear systems and have numerous tuning parameters. Here, we present a framework for learning a parameterized analysis map - the transformation that takes samples from a forecast distribution, and combines with an observation, to update the approximate filtering distribution - using variational inference. In principle this can lead to a better approximation of the filtering distribution, and hence smaller bias. We show that this methodology can be used to learn the gain matrix, in an affine analysis map, for filtering linear and nonlinear dynamical systems; we also study the learning of inflation and localization parameters for an EnKF. The framework developed here can also be used to learn new filtering algorithms with more general forms for the analysis map.