2 papers
math.AP2026
Direct and Indirect Physics-Informed Neural Networks for Dirichlet Boundary Control of Semilinear Parabolic Equations: A Conditional Error Analysis
Nguyen Thanh Quang, Ta Thi Thanh Mai, Bui Xuan Dieu
We study physics-informed neural networks (PINNs) for the Dirichlet boundary control of a semilinear parabolic equation with Tikhonov regularization. Two approaches are considered.…
math.AP2026
Tikhonov-Regularized Physics-Informed Neural Networks for Terminal-State Distributed Optimal Control of Parabolic Partial Differential Equations
Nguyen Thanh Quang, Ta Thi Thanh Mai
In this study, we propose a Physics-Informed Neural Networks (PINNs) framework that incorporates Tikhonov regularization to solve terminal-state tracking optimal control constraine…