3 papers
math.NA2026
A Priori Error Bounds for Boundary-Adapted PINNs Solving Elliptic Dirichlet Problems
Nathanael Tepakbong, Jun Fan, Xiang Zhou +1
We study the numerical resolution of uniformly elliptic Dirichlet boundary value problems (BVPs) by minimization of the PDE residual over a hypothesis space of Neural Networks made…
stat.ML2026
Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds
Nathanael Tepakbong, Hanyu Hu, Chengyu Liu +1
Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-con…
cs.LG2025
Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition
Nathanael Tepakbong, Xiang Zhou, Ding-Xuan Zhou
We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent , as well as its l…