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Optimal control of parametric partial differential equations (PDEs) is crucial in many applications in engineering and science. In recent years, the progress in scientific machine learning has opened up new frontiers for the control of…

Machine Learning · Computer Science 2024-10-10 Nicolò Botteghi , Urban Fasel

Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how to use RL to tackle more general PDE control problems that…

Machine Learning · Computer Science 2018-06-20 Yangchen Pan , Amir-massoud Farahmand , Martha White , Saleh Nabi , Piyush Grover , Daniel Nikovski

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in complex environments, such as stabilizing a tokamak fusion reactor or minimizing the drag force on an object in a…

Machine Learning · Computer Science 2025-08-26 Nicholas Zolman , Christian Lagemann , Urban Fasel , J. Nathan Kutz , Steven L. Brunton

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…

Machine Learning · Computer Science 2023-12-27 Sebastian Peitz , Jan Stenner , Vikas Chidananda , Oliver Wallscheid , Steven L. Brunton , Kunihiko Taira

Deep Reinforcement Learning (DRL) has become a popular method for solving control problems in power systems. Conventional DRL encourages the agent to explore various policies encoded in a neural network (NN) with the goal of maximizing the…

Systems and Control · Electrical Eng. & Systems 2024-10-28 Tong Wu , Anna Scaglione , Daniel Arnold

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

Numerical Analysis · Mathematics 2021-09-07 Ricardo A. Delgadillo , Jingwei Hu , Haizhao Yang

Deep Reinforcement Learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control…

We introduce a reinforcement learning (RL) environment to design and benchmark control strategies aimed at reducing drag in turbulent fluid flows enclosed in a channel. The environment provides a framework for computationally-efficient,…

Fluid Dynamics · Physics 2023-02-09 L. Guastoni , J. Rabault , P. Schlatter , H. Azizpour , R. Vinuesa

Rotating detonation engines (RDEs) are a promising propulsion concept that may offer higher thermodynamic efficiency and specific impulse than conventional systems, but nonlinear phenomena, including transitions to oscillatory or chaotic…

Fluid Dynamics · Physics 2026-04-17 Kristian Holme , Jean Rabault , Ricardo Vinuesa , Mikael Mortensen

This review addresses the problem of learning abstract representations of the measurement data in the context of Deep Reinforcement Learning (DRL). While the data are often ambiguous, high-dimensional, and complex to interpret, many…

Machine Learning · Computer Science 2024-05-31 Nicolò Botteghi , Mannes Poel , Christoph Brune

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

Optimization and Control · Mathematics 2024-01-04 Daokuan Zhu , Tianqi Xu , Jie Lu

Distribution system state estimation (DSSE) is paramount for effective state monitoring and control. However, stochastic outputs of renewables and asynchronous streaming of multi-rate measurements in practical systems largely degrade the…

Systems and Control · Electrical Eng. & Systems 2023-10-23 Ying Zhang , Junbo Zhao , Di Shi , Sungjoo Chung

This article proposes a model-based deep reinforcement learning (DRL) method to design emergency control strategies for short-term voltage stability problems in power systems. Recent advances show promising results in model-free DRL-based…

Systems and Control · Electrical Eng. & Systems 2022-12-07 Ramij R. Hossain , Tianzhixi Yin , Yan Du , Renke Huang , Jie Tan , Wenhao Yu , Yuan Liu , Qiuhua Huang

This article presents a motion planning and control framework for flexible robotic manipulators, integrating deep reinforcement learning (DRL) with a nonlinear partial differential equation (PDE) controller. Unlike conventional approaches…

Robotics · Computer Science 2025-06-11 Amir Hossein Barjini , Seyed Adel Alizadeh Kolagar , Sadeq Yaqubi , Jouni Mattila

This work reports the application of a model-free deep-reinforcement-learning-based (DRL) flow control strategy to suppress perturbations evolving in the 1-D linearised Kuramoto-Sivashinsky (KS) equation and 2-D boundary layer flows. The…

Fluid Dynamics · Physics 2023-01-18 Da Xu , Mengqi Zhang

Deep reinforcement learning (DRL) has gained great success by learning directly from high-dimensional sensory inputs, yet is notorious for the lack of interpretability. Interpretability of the subtasks is critical in hierarchical…

Artificial Intelligence · Computer Science 2019-03-01 Daoming Lyu , Fangkai Yang , Bo Liu , Steven Gustafson

In this work, we devise a new, general-purpose reinforcement learning strategy for the optimal control of parametric dynamical systems. Such problems frequently arise in applied sciences and engineering and entail a significant complexity…

Machine Learning · Computer Science 2026-02-12 Nicolò Botteghi , Stefania Fresca , Mengwu Guo , Andrea Manzoni

Real-time control of pumps can be an infeasible task in water distribution systems (WDSs) because the calculation to find the optimal pump speeds is resource-intensive. The computational need cannot be lowered even with the capabilities of…

Artificial Intelligence · Computer Science 2020-10-14 Gergely Hajgató , György Paál , Bálint Gyires-Tóth

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…

Machine Learning · Computer Science 2021-12-09 Erfan Pirmorad , Faraz Khoshbakhtian , Farnam Mansouri , Amir-massoud Farahmand

Turbulent-flow control aims to develop strategies that effectively manipulate fluid systems, such as the reduction of drag in transportation and enhancing energy efficiency, both critical steps towards reducing global CO$_2$ emissions. Deep…

Fluid Dynamics · Physics 2026-05-25 Miguel Beneitez , Andres Cremades , Luca Guastoni , Ricardo Vinuesa
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