A Unified Interface Neural Network for Elliptic Interface Problems
Abstract
We develop a Unified Interface Neural Network (UINN) framework for elliptic interface problems with discontinuous coefficients. A single shared network provides a unified representation of the solution in both subdomains, while a projection--correction construction embeds the solution and flux jump conditions directly into the neural trial space. This design aligns with the classical numerical principle of incorporating interfacial physics into the approximation basis to construct interface-unfitted numerical methods. The jump conditions are therefore satisfied exactly for any network parameters. Compared with methods based on separate phase networks and numerical formulations with interface penalty terms, UINN provides a unified representation with exact enforcement of interfacial jump conditions and interface-penalty-free optimization. Those features streamline the numerical formulations and can enhance training robustness. Numerical experiments on smooth interfaces at modestly large and high coefficient contrasts demonstrate UINN's solution accuracy, near-machine-precision satisfaction of the interface jump conditions, and enhanced robustness.
Related
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BibTeX
@misc{zhuang2026unified,
title = {{A Unified Interface Neural Network for Elliptic Interface Problems}},
author = {Qiao Zhuang and Xu Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25409},
eprint = {2610.25409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25409},
}
RIS
TY - UNPB
TI - A Unified Interface Neural Network for Elliptic Interface Problems
AU - Qiao Zhuang
AU - Xu Zhang
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25409
UR - https://arxiv.org/abs/2610.25409
AB - We develop a Unified Interface Neural Network (UINN) framework for elliptic interface problems with discontinuous coefficients. A single shared network provides a unified representation of the solution in both subdomains, while a projection--correction construction embeds the solution and flux jump conditions directly into the neural trial space. This design aligns with the classical numerical principle of incorporating interfacial physics into the approximation basis to construct interface-unfitted numerical methods. The jump conditions are therefore satisfied exactly for any network parameters. Compared with methods based on separate phase networks and numerical formulations with interface penalty terms, UINN provides a unified representation with exact enforcement of interfacial jump conditions and interface-penalty-free optimization. Those features streamline the numerical formulations and can enhance training robustness. Numerical experiments on smooth interfaces at modestly large and high coefficient contrasts demonstrate UINN's solution accuracy, near-machine-precision satisfaction of the interface jump conditions, and enhanced robustness.
ER -