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Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systems
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The purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop in detail the underlying ideas in the setting of linear stochastic systems with Gaussian noise and recover known results.
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Gradient Flow Algorithms for Density Propagation in Stochastic Systems
A Sinkhorn-type proximal recursion, proved contractive in the Thompson metric, computes transient Fokker-Planck and McKean-Vlasov densities on weighted point clouds without spatial discretization.
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