# Deterministic particle flows for constraining SDEs

arXiv: https://arxiv.org/abs/2110.13020 · HTML: https://mlsanity.com/paper/2110.13020/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems](https://mlsanity.com/paper/2301.08102/) (2023)
- [Geometric constraints improve inference of sparsely observed stochastic dynamics](https://mlsanity.com/paper/2304.00423/) (2023)

## Abstract (arXiv)

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.