Interpretable and efficient data-driven discovery and control of distributed systems
Author(s)
Wolf, Florian
Botteghi, Nicolo
Fasel, Urban
Manzoni, Andrea
Type
Journal Article
Abstract
Effectively controlling systems governed by partial differential equations (PDEs) is crucial in several fields of applied sciences and engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement learning (RL), particularly deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges, including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these challenges, we propose a data-efficient, interpretable, and scalable Dyna-style model-based RL framework specifically tailored for PDE control. Our approach integrates Sparse Identification of Nonlinear Dynamics with Control within an Autoencoder-based dimensionality reduction scheme for PDE states and actions (AE+SINDy-C). This combination enables fast rollouts with significantly fewer environment interactions while providing an interpretable latent space representation of the PDE dynamics, facilitating insight into the control process. We validate our method on two PDE problems describing fluid flows—namely, the 1D Burgers equation and 2D Navier–Stokes equations—comparing it against a model-free baseline. Our extensive analysis highlights improved sample efficiency, stability, and interpretability in controlling complex PDE systems.
Date Issued
2025-11-14
Date Acceptance
2025-09-06
Citation
Data-Centric Engineering, 2025, 6
ISSN
2632-6736
Publisher
Cambridge University Press
Journal / Book Title
Data-Centric Engineering
Volume
6
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Identifier
10.1017/dce.2025.10027
Subjects
autoencoder
Computer Science
Computer Science, Artificial Intelligence
Computer Science, Interdisciplinary Applications
Engineering
Engineering, Multidisciplinary
model-based deep reinforcement learning
Science & Technology
sparse identification of nonlinear dynamics
Technology
Publication Status
Published
Article Number
e51
Date Publish Online
2025-11-14