A Domain-specific adaptation network for elliptic interface problems
Abstract
Deep learning provides a flexible mesh-free framework for solving elliptic interface problems. However, domain-specific neural approaches often rely on separate networks for individual subdomains, causing the model complexity to grow rapidly as the number of subdomains increases. To address this limitation, we propose a Domain-Specific Adaptation Network (DSAN), which combines a shared backbone with lightweight subdomain-specific adapters to provide local represen- representation flexibility without replicating a complete network for each subdomain. We further establish a stability and error analysis showing that the continuous physics-informed residual controls the solution error, and decompose the resulting error into approximation, optimization, and sampling components. Numerical experiments on two- and three-dimensional problems with multiple regular and irregular interfaces demonstrate that DSAN achieves accuracy comparable to or better than fully decomposed multi-network methods while requiring substantially fewer trainable parameters. More- over, the parameter savings become increasingly pronounced as the number of subdomains grows, demonstrating the scalability of the proposed domain-specific adaptation framework.
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BibTeX
@misc{luo2026domainspecific,
title = {{A Domain-specific adaptation network for elliptic interface problems}},
author = {Jiaqi Luo and Hongmei Kang and Xingye Yue and Shixin Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14887},
eprint = {2610.14887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14887},
}
RIS
TY - UNPB
TI - A Domain-specific adaptation network for elliptic interface problems
AU - Jiaqi Luo
AU - Hongmei Kang
AU - Xingye Yue
AU - Shixin Xu
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14887
UR - https://arxiv.org/abs/2610.14887
AB - Deep learning provides a flexible mesh-free framework for solving elliptic interface problems. However, domain-specific neural approaches often rely on separate networks for individual subdomains, causing the model complexity to grow rapidly as the number of subdomains increases. To address this limitation, we propose a Domain-Specific Adaptation Network (DSAN), which combines a shared backbone with lightweight subdomain-specific adapters to provide local represen- representation flexibility without replicating a complete network for each subdomain. We further establish a stability and error analysis showing that the continuous physics-informed residual controls the solution error, and decompose the resulting error into approximation, optimization, and sampling components. Numerical experiments on two- and three-dimensional problems with multiple regular and irregular interfaces demonstrate that DSAN achieves accuracy comparable to or better than fully decomposed multi-network methods while requiring substantially fewer trainable parameters. More- over, the parameter savings become increasingly pronounced as the number of subdomains grows, demonstrating the scalability of the proposed domain-specific adaptation framework.
ER -