2024-06-11-bhan24a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
PDE control gym: A benchmark for data-driven boundary control of partial differential equations	Over the last decade, data-driven methods have surged in popularity, emerging as valuable tools for control theory. As such, neural network approximations of control feedback laws, system dynamics, and even Lyapunov functions have attracted growing attention. With the ascent of learning based control, the need for accurate, fast, and easy-to-use benchmarks has increased. In this work, we present the first learning-based environment for boundary control of PDEs. In our benchmark, we introduce three foundational PDE problems — a 1D transport PDE, a 1D reaction-diffusion PDE, and a 2D Navier–Stokes PDE — whose solvers are bundled in an user-friendly reinforcement learning gym. With this gym, we then present the first set of model-free, reinforcement learning algorithms for solving this series of benchmark problems, achieving stability, although at a higher cost compared to model-based PDE backstepping. With the set of benchmark environments and detailed examples, this work significantly lowers the barrier to entry for learning-based PDE control — a topic largely unexplored by the data-driven control community. The entire benchmark is available on Github along with detailed documentation and the presented reinforcement learning models are open sourced.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bhan24a	0	{PDE} control gym: {A} benchmark for data-driven boundary control of partial differential equations	1083	1095	1083-1095	1083	false	Bhan, Luke and Bian, Yuexin and Krstic, Miroslav and Shi, Yuanyuan	given family Luke Bhan given family Yuexin Bian given family Miroslav Krstic given family Yuanyuan Shi	2024-06-11		Proceedings of the 6th Annual Learning for Dynamics & Control Conference	242	inproceedings	date-parts 2024 6 11	https://proceedings.mlr.press/v242/bhan24a/bhan24a.pdf