Resources

Speaker: Ricardo Baptista with Caltech

Solving filtering and smoothing problems for geophysical applications involve estimating the hidden states of complex systems and accurately characterizing their uncertainty. Popular algorithms for tackling these problems include ensemble Kalman methods such as the EnKF, EnKS and RTS smoother. While these algorithms yield robust state estimates for high-dimensional models with non-Gaussian statistics, ensemble Kalman methods are limited by linear transformations and are generally inconsistent with the true Bayesian solution. In this presentation, I will discuss how measure transport can be used to consistently transform a prior ensemble into samples from a filtering or smoothing distribution. This approach provides a natural generalization of Kalman methods to nonlinear transformations, thereby reducing the intrinsic bias of classic algorithms with a marginal increase in computational cost. In small-sample settings, I will show how to estimate transport maps for high-dimensional inference problems by exploiting low-dimensional structure in the target distribution. Finally, I will demonstrate the benefit of this framework for filtering and smoothing on chaotic dynamical systems and aerodynamic flows.