Deterministic particle flows for constraining SDEs
Abstract
Devising optimal interventions for diffusive systems often requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation, a nonlinear backward partial differential equation (PDE), that is, in general, nontrivial to solve. Existing control methods either tackle the HJB directly with grid-based PDE solvers, or resort to iterative stochastic path sampling to obtain the necessary controls. Here, we present a framework that interpolates between these two approaches. By reformulating the optimal interventions in terms of logarithmic gradients ( scores ) of two forward probability flows, and by employing deterministic particle methods for solving Fokker-Planck equations, we introduce a novel fully deterministic framework that computes the required optimal interventions in one shot.
Cite
@article{arxiv.2110.13020,
title = {Deterministic particle flows for constraining SDEs},
author = {Dimitra Maoutsa and Manfred Opper},
journal= {arXiv preprint arXiv:2110.13020},
year = {2022}
}
Comments
4+3 pages, 2 figures -- workshop paper -- Machine Learning and the Physical Sciences, Workshop at the 35th Conference on Neural Information Processing Systems (NeurIPS 2021) The related journal paper is published here: https://link.aps.org/doi/10.1103/PhysRevResearch.4.043035