# Solving a class of stochastic optimal control problems by physics-informed neural networks

arXiv: https://arxiv.org/abs/2402.15592 · HTML: https://mlsanity.com/paper/2402.15592/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 23 Feb 2024.

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

- [Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space](https://mlsanity.com/paper/2005.05409/) (2020)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Deep Learning Methods for Mean Field Control Problems with Delay](https://mlsanity.com/paper/1905.00358/) (2019)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [A Neural Network Approach for Stochastic Optimal Control](https://mlsanity.com/paper/2209.13104/) (2022)
- [Learning Optimal Control via Forward and Backward Stochastic Differential Equations](https://mlsanity.com/paper/1509.02195/) (2015)
- [Solving stochastic optimal control problem via stochastic maximum principle with deep learning method](https://mlsanity.com/paper/2007.02227/) (2020)
- [Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver](https://mlsanity.com/paper/2010.09988/) (2020)
- [Deep 2FBSDEs For Systems With Control Multiplicative Noise](https://mlsanity.com/paper/1906.04762/) (2019)

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

- [Error analysis for the deep Kolmogorov method](https://mlsanity.com/paper/2508.17167/) (2025)

## Abstract (arXiv)

The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the feedback control and the value function using a decoupled neural network with multiple outputs. We train this network by using a loss function with penalty terms that enforce the HJB equation along the sampled trajectories generated by the controlled system. More significantly, numerical results on various applications are carried out to demonstrate that the proposed approach is efficient and applicable.