Author

T. Mai

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Preprint Sep 2026

Direct and Indirect Physics-Informed Neural Networks for Dirichlet Boundary Control of Semilinear Parabolic Equations: A Conditional Error Analysis

This work develops an error estimation framework that decomposes the total error into approximation, optimization, quadrature, and soft boundary/terminal-constraint contributions and derives a quantitative linearized stability estimate and a conditional local nonlinear residual-to-error estimate.

Q. Nguyen, T. Mai, Dieu Xuan Bui · 0 citations

Preprint Jul 2026

Tikhonov-Regularized Physics-Informed Neural Networks for Terminal-State Distributed Optimal Control of Parabolic Partial Differential Equations

A regularized PINNs framework that incorporates Tikhonov regularization to solve terminal-state tracking optimal control constrained by parabolic partial differential equations is proposed, establishing a consistency result showing that PINNs minimizers nearly attain the continuous regularized objective under residual...

Q. Nguyen, T. Mai · 1 citation