Efficient and Accurate Lift-and-Decoupling Generalized Transferable Neural Networks for Elliptic and Moving Interface Problems
Abstract
In this paper, we propose a highly efficient and accurate method, called ``lift-and-decoupling generalized transferable neural network" (LD-GTransNet), for numerical solution of elliptic and moving interface problems. Our method makes use of the multi-layer GTransNet approach and incorporates a novel {lift-and-decoupling} strategy, in which the hidden-layer neuron parameters are preset and the physical coordinates and the added auxiliary variable are processed by separate subnetworks. Such design enables a unified global approximation of piecewise smooth solutions without explicit domain decomposition, while preserving network expressivity and avoiding the redundancy inherent in conventional {lift} approaches. The resulting formulation reduces to a linear least-squares problem, thereby eliminating the need of nonlinear training and ensuring the high computational efficiency and accuracy. Extensive numerical experiments on benchmark interface problems in two and three dimensions demonstrate that, compared with existing neural network-based and traditional numerical methods, our proposed LD-GTransNet consistently delivers superior performance, particularly for problems with high-contrast coefficients and complex interface geometries.
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BibTeX
@misc{cheng2026efficient,
title = {{Efficient and Accurate Lift-and-Decoupling Generalized Transferable Neural Networks for Elliptic and Moving Interface Problems}},
author = {Tao Cheng and Junqing Jia and Lili Ju and Xiaoping Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02891},
eprint = {2610.02891},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02891},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient and Accurate Lift-and-Decoupling Generalized Transferable Neural Networks for Elliptic and Moving Interface Problems
AU - Tao Cheng
AU - Junqing Jia
AU - Lili Ju
AU - Xiaoping Zhang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02891
UR - https://arxiv.org/abs/2610.02891
AB - In this paper, we propose a highly efficient and accurate method, called ``lift-and-decoupling generalized transferable neural network" (LD-GTransNet), for numerical solution of elliptic and moving interface problems. Our method makes use of the multi-layer GTransNet approach and incorporates a novel {lift-and-decoupling} strategy, in which the hidden-layer neuron parameters are preset and the physical coordinates and the added auxiliary variable are processed by separate subnetworks. Such design enables a unified global approximation of piecewise smooth solutions without explicit domain decomposition, while preserving network expressivity and avoiding the redundancy inherent in conventional {lift} approaches. The resulting formulation reduces to a linear least-squares problem, thereby eliminating the need of nonlinear training and ensuring the high computational efficiency and accuracy. Extensive numerical experiments on benchmark interface problems in two and three dimensions demonstrate that, compared with existing neural network-based and traditional numerical methods, our proposed LD-GTransNet consistently delivers superior performance, particularly for problems with high-contrast coefficients and complex interface geometries.
ER -