Year: 2025
Type: article
Abstract: 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).
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: MATH-DT: Advancing Digital Twins for Jet Engines Through Mathematical and Computational Innovation, G1453181110, G1816068141, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, FAST OUTER LOOP SOLUTION ALGORITHMS BASED ON A COHERENT COUPLING OF PHYSICAL AND MACHINE LEARNING MODELS, Hybrid Time Integration Algorithms for Co-Simulation of Multiscale Multiphysics Systems, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, G5785005040, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI
OpenAlex ID: W4413299174