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Selective boundary condition reduction via learned error gating
Abstract
Parametric PDEs can admit different boundary conditions with different accuracy and computational cost. We introduce a framework for learning when one reduced boundary condition can replace another: paired solutions train a neural network to estimate the resulting domain and boundary errors, and the simpler condition is used only when both predicted errors meet prescribed tolerances. We focus on singular limits in applications, in which a stiff Robin or nonlinear boundary law is replaced by its limiting Dirichlet form. We evaluate the method on a galvanic corrosion problem and other nonlinear stationary and evolution problems.
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BibTeX
@misc{fernandez2026selective,
title = {{Selective boundary condition reduction via learned error gating}},
author = {Daniel Fernández and Dominik Penk and Dominik Riedelbauch},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08461},
eprint = {2609.08461},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08461},
}
RIS
TY - UNPB
TI - Selective boundary condition reduction via learned error gating
AU - Daniel Fernández
AU - Dominik Penk
AU - Dominik Riedelbauch
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08461
UR - https://arxiv.org/abs/2609.08461
AB - Parametric PDEs can admit different boundary conditions with different accuracy and computational cost. We introduce a framework for learning when one reduced boundary condition can replace another: paired solutions train a neural network to estimate the resulting domain and boundary errors, and the simpler condition is used only when both predicted errors meet prescribed tolerances. We focus on singular limits in applications, in which a stiff Robin or nonlinear boundary law is replaced by its limiting Dirichlet form. We evaluate the method on a galvanic corrosion problem and other nonlinear stationary and evolution problems.
ER -