# Rare Event Analysis via Stochastic Optimal Control

arXiv: https://arxiv.org/abs/2604.13213 · HTML: https://mlsanity.com/paper/2604.13213/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 61 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control](https://mlsanity.com/paper/2508.10684/) (2025)
- [A Taxonomy of Loss Functions for Stochastic Optimal Control](https://mlsanity.com/paper/2410.00345/) (2024)
- [Solving Time-Continuous Stochastic Optimal Control Problems: Algorithm Design and Convergence Analysis of Actor-Critic Flow](https://mlsanity.com/paper/2402.17208/) (2024)
- [Deep Learning Method for Computing Committor Functions with Adaptive Sampling](https://mlsanity.com/paper/2404.06206/) (2024)
- [A semigroup method for high dimensional committor functions based on neural network](https://mlsanity.com/paper/2012.06727/) (2020)
- [Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Paths](https://mlsanity.com/paper/2501.15522/) (2025)
- [An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Control](https://mlsanity.com/paper/2410.05163/) (2024)
- [Reinforcement Learning with Random Time Horizons](https://mlsanity.com/paper/2506.00962/) (2025)

## Built on by (most cited first, 4 of 4)

- [Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events](https://mlsanity.com/paper/2606.06295/) (2026)
- [Machine learning kinetics from molecular dynamics data](https://mlsanity.com/paper/2609.17736/) (2026)
- [ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation](https://mlsanity.com/paper/2610.02538/) (2026)
- [Transition Path Sampling Using Koopman Operators and Exit-Time Optimal Control](https://mlsanity.com/paper/2610.10054/) (2026)

## Abstract (arXiv)

Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased simulations seldom produce them. Transition Path Theory (TPT) provides a rigorous statistical framework for analyzing such events: it characterizes the ensemble of reactive trajectories between two designated metastable states (reactant and product), and its central object--the committor function, which gives the probability that the system will next reach the product rather than the reactant--encodes all essential kinetic and thermodynamic information. We introduce a framework that casts committor estimation as a stochastic optimal control (SOC) problem. In this formulation the committor defines a feedback control--proportional to the gradient of its logarithm--that actively steers trajectories toward the reactive region, thereby enabling efficient sampling of reactive paths. To solve the resulting hitting-time control problem we develop two complementary objectives: a direct backpropagation loss and a principled off-policy Value Matching loss, for which we establish first-order optimality guarantees. We further address metastability, which can trap controlled trajectories in intermediate basins, by introducing an alternative sampling process that preserves the reactive current while lowering effective energy barriers. On benchmark systems, the framework yields markedly more accurate committor estimates, reaction rates, and equilibrium constants than existing methods.