Nathanael Tepakbong

collaborators

3 papers

math.NA2026

Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^{2} (Ω)$ A Priori Error Bounds with Application to Mean Escape Time Computation

Nathanael Tepakbong, Jun Fan, Xiang Zhou +1

Motivated by the numerical computation of the Mean Escape Time (MET) $τ : Ω \to R$ of a stochastic process from a bounded domain $Ω \subseteq R^{d}$ , we study elliptic Di…

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 $q > 0$ , as well as its l…

Boundary-Adapted PINNs for Elliptic Dirichlet Problems: H2(Ω) A Priori Error Bounds with Application to Mean Escape Time Computation

Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds

Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition

Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^{2} (Ω)$ A Priori Error Bounds with Application to Mean Escape Time Computation