Solving PDE-Constrained Control Problems Using Operator Learning
Keywords:Domain(s) Of Application (APP), Constraint Satisfaction And Optimization (CSO)
AbstractThe modeling and control of complex physical systems are essential in real-world problems. We propose a novel framework that is generally applicable to solving PDE-constrained optimal control problems by introducing surrogate models for PDE solution operators with special regularizers. The procedure of the proposed framework is divided into two phases: solution operator learning for PDE constraints (Phase 1) and searching for optimal control (Phase 2). Once the surrogate model is trained in Phase 1, the optimal control can be inferred in Phase 2 without intensive computations. Our framework can be applied to both data-driven and data-free cases. We demonstrate the successful application of our method to various optimal control problems for different control variables with diverse PDE constraints from the Poisson equation to Burgers' equation.
How to Cite
Hwang, R., Lee, J. Y., Shin, J. Y., & Hwang, H. J. (2022). Solving PDE-Constrained Control Problems Using Operator Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 36(4), 4504-4512. https://doi.org/10.1609/aaai.v36i4.20373
AAAI Technical Track on Domain(s) Of Application