Physics-Informed Neural Networks for PDE-Constrained Optimization and Control

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

doi:10.1007/s42967-025-00499-x

Physics-Informed Neural Networks for PDE-Constrained Optimization and Control

Journal Article · Mon Aug 18 00:00:00 EDT 2025 · Communications on Applied Mathematics and Computation

DOI:https://doi.org/10.1007/s42967-025-00499-x· OSTI ID:3028301

^[1]; Sarshar, Arash ^[2]; Popov, Andrey A. ^[3]; Sandu, Adrian ^[1]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
California State Univ., Long Beach, CA (United States)
Univ. of Hawaii at Manoa, Honolulu, HI (United States)

The goal of optimal control is to determine a sequence of inputs for maximizing or minimizing a given performance criterion subject to the dynamics and constraints of the system under observation. This work introduces Control Physics-Informed Neural Networks (PINNs), which simultaneously learn both the system states and the optimal control signal in a single-stage framework that leverages the system’s underlying physical laws. While prior approaches often follow a two-stage process-modeling, the system first and then devising its control—the presented novel framework embeds the necessary optimality conditions directly into the network architecture and loss function. We demonstrate the effectiveness of the novel methodology by solving various open-loop optimal control problems governed by analytical, one-dimensional, and two-dimensional partial differential equations (PDEs).

View Accepted Manuscript (DOE)

Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0021313

Other Award/Contract Number:: DMS-2411069
NSF DMS-2436357

OSTI ID:: 3028301

Journal Information:: Communications on Applied Mathematics and Computation, Journal Name: Communications on Applied Mathematics and Computation; ISSN 2096-6385; ISSN 2661-8893

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Physics-informed neural networks (PINNs)
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