# Deep Reinforcement Learning for Online Control of Stochastic Partial Differential Equations

arXiv: https://arxiv.org/abs/2110.11265 · HTML: https://mlsanity.com/paper/2110.11265/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 19 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Reinforcement Learning with Function-Valued Action Spaces for Partial Differential Equation Control](https://mlsanity.com/paper/1806.06931/) (2018)

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

- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)
- [Dynamic Noises of Multi-Agent Environments Can Improve Generalization: Agent-based Models meets Reinforcement Learning](https://mlsanity.com/paper/2204.14076/) (2022)
- [SDGym: Low-Code Reinforcement Learning Environments using System Dynamics Models](https://mlsanity.com/paper/2310.12494/) (2023)
- [A Method to Improve the Performance of Reinforcement Learning Based on the Y Operator for a Class of Stochastic Differential Equation-Based Child-Mother Systems](https://mlsanity.com/paper/2311.04014/) (2023)

## Abstract (arXiv)

In many areas, such as the physical sciences, life sciences, and finance, control approaches are used to achieve a desired goal in complex dynamical systems governed by differential equations. In this work we formulate the problem of controlling stochastic partial differential equations (SPDE) as a reinforcement learning problem. We present a learning-based, distributed control approach for online control of a system of SPDEs with high dimensional state-action space using deep deterministic policy gradient method. We tested the performance of our method on the problem of controlling the stochastic Burgers' equation, describing a turbulent fluid flow in an infinitely large domain.