# Online identification and control of PDEs via Reinforcement Learning methods

arXiv: https://arxiv.org/abs/2308.04068 · HTML: https://mlsanity.com/paper/2308.04068/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2023.

## Built on by (most cited first, 5 of 5)

- [Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems](https://mlsanity.com/paper/2411.04098/) (2024)
- [Soft Actor-Critic with Backstepping-Pretrained DeepONet for control of PDEs](https://mlsanity.com/paper/2507.04232/) (2025)
- [LinguaFluid: Language Guided Fluid Control via Semantic Rewards in Reinforcement Learning](https://mlsanity.com/paper/2508.05977/) (2025)
- [Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems](https://mlsanity.com/paper/2606.12337/) (2026)
- [Backstepping-Guided Reinforcement Learning for Wide-Range Saint-Venant Canal Regulation](https://mlsanity.com/paper/2608.20089/) (2026)

## Abstract (arXiv)

We focus on the control of unknown Partial Differential Equations (PDEs). The system dynamics is unknown, but we assume we are able to observe its evolution for a given control input, as typical in a Reinforcement Learning framework. We propose an algorithm based on the idea to control and identify on the fly the unknown system configuration. In this work, the control is based on the State-Dependent Riccati approach, whereas the identification of the model on Bayesian linear regression. At each iteration, based on the observed data, we obtain an estimate of the a-priori unknown parameter configuration of the PDE and then we compute the control of the correspondent model. We show by numerical evidence the convergence of the method for infinite horizon control problems.