# Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning

arXiv: https://arxiv.org/abs/2209.13098 · HTML: https://mlsanity.com/paper/2209.13098/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 39 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise](https://mlsanity.com/paper/2005.03769/) (2020)
- [Convergence Rate for the Ordered Upwind Method](https://mlsanity.com/paper/1601.02885/) (2016)

## Built on by (most cited first, 1 of 1)

- [Sparse identification of quasipotentials via a combined data-driven method](https://mlsanity.com/paper/2407.05050/) (2024)

## Abstract (arXiv)

The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientific fields. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to achieve a desired value based on the quasipotential concept and machine learning. Specifically, we develop a neural network architecture to compute the global quasipotential function. Then we design a systematic iterated numerical algorithm to calculate the controller for a given mean exit time. Moreover, we identify the most probable path between metastable attractors with help of the effective Hamilton-Jacobi scheme and the trained neural network. Numerical experiments demonstrate that our control strategy is effective and sufficiently accurate.