2023/09/16 by Daniel Grange, Grange, Daniel, Mohammad Al‐Jarrah +9
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2309.08847
In this paper we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on manifolds. Specializing these maps for sampling conditional probability distributions provides an ensemble approach for solving nonlinear filtering problems defined on such geometries. The proposed computational methodology is illustrated with examples of transport and nonlinear filtering on Lie groups, including the circle S1, the special Euclidean group SE(2), and the special orthogonal group SO(3).