CMX Student/Postdoc Seminar

Sequential inference problems are ubiquitous in scientific applications ranging from operational aspects of numerical weather prediction to tracking infectious diseases. Given a sequence of observations, the ensemble Kalman filter (EnKF) is a widely popular online algorithm for estimating the hidden state of these systems and their uncertainty. While the EnKF yields robust state estimates for many high-dimensional and non-Gaussian models, this method is limited by linear transformations and is generally inconsistent with the Bayesian solution. In this presentation, we will discuss how transportation of measures can be used to consistently transform a forecast ensemble into samples from the filtering distribution. This approach can be understood as a natural generalization of the EnKF to nonlinear updates, and reduces the intrinsic bias of the EnKF with a marginal increase in computational cost. In small-sample settings, we will show how to estimate transport maps for high-dimensional inference problems by exploiting low-dimensional structure in the filtering distribution. Finally, we will demonstrate the benefit of this framework for filtering with chaotic dynamical systems and aerodynamic flows.