Work

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

Year: 2022

Type: preprint

Abstract: A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously solve for a given system state, and for the optimal control signal, in a one-stage framework that conforms to the underlying physical laws. Prior approaches use a two-stage framework that first models and then controls a system in sequential order. In contrast, a Control PINN incorporates the required optimality conditions in its architecture and in its 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2205.03377

Authors: Barry-Straume, Jostein, Sarshar, Arash, Popov, Andrey A., Sandu, Adrian

Institution: Virginia Tech

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Advanced Scientific Computing Research

Awards: G1816068141, Transforming Reduced-Order Models of Fluids with Data Assimilation, FAST OUTER LOOP SOLUTION ALGORITHMS BASED ON A COHERENT COUPLING OF PHYSICAL AND MACHINE LEARNING MODELS, G3440263237, G5785005040

OpenAlex ID: W4229459499

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Cited by: 2

Related to: 10