# Reinforcement learning for control of partial differential equations

**Authors:** Nicolò Botteghi, Matteo Tomasetto, Andrea Manzoni  
**Lab:** Politecnico di Milano · **Published:** 29 Oct 2026  
**Links:** [arXiv](https://arxiv.org/abs/2610.40449) · [PDF](https://arxiv.org/pdf/2610.40449) · [This page](https://omen-bit.github.io/ai-paper-daily/paper/2610.40449.html)

## Abstract

Controlling dynamical systems governed by partial differential equations (PDEs) remains a challenging task in scientific computing, owing to high-dimensional state spaces, distributed actuation, nonlinear dynamics, and stringent real-time constraints. Reinforcement learning (RL) has emerged as a promising paradigm for synthesizing feedback controllers that adapt to varying operating conditions and can be deployed efficiently in real-time. This review provides a unified perspective on RL and PDE-constrained optimization, and surveys model-free, model-based, and multi-agent RL approaches to PDE control, with particular emphasis on sample efficiency, generalization across parametric variations, and scalability to high-dimensional problems. Two demonstrative examples, the stabilization of a chaotic system and a flow control problem, illustrate the performance and pitfalls of RL agents in practice. Finally, we discuss evaluation and benchmarking practices, current limitations, and open research directions toward reliable, data-efficient, and scalable RL for scientific computing.

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