Physics-informed neural networks for PDE-constrained optimization and control

• URL: http://arxiv.org/abs/2205.03377v1
• Date: Fri, 6 May 2022 17:22:36 GMT
• Title: Physics-informed neural networks for PDE-constrained optimization and control
• Authors: Jostein Barry-Straume, Arash Sarshar, Andrey A. Popov, and Adrian Sandu
• Abstract summary: Control Physics-Informed Neural Networks simultaneously solve a given system state, and its respective optimal control. The success of Control PINNs is demonstrated by solving the following open-loop optimal control problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A fundamental problem of science is designing optimal control policies that manipulate a given environment into producing a desired outcome. Control Physics-Informed Neural Networks simultaneously solve a given system state, and its respective optimal control, in a one-stage framework that conforms to physical laws of the system. Prior approaches use a two-stage framework that models and controls a system sequentially, whereas Control PINNs incorporates the required optimality conditions in its architecture and loss function. The success of Control PINNs is demonstrated by solving the following open-loop optimal control problems: (i) an analytical problem (ii) a one-dimensional heat equation, and (iii) a two-dimensional predator-prey problem.

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