Selective boundary condition reduction via learned error gating

Daniel Fernández; Dominik Penk; Dominik Riedelbauch

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arXiv · 2609.08461

Selective boundary condition reduction via learned error gating

Daniel Fernández·Dominik Penk·Dominik Riedelbauch

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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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Daniel Fernández, Dominik Penk, Dominik Riedelbauch. 2026-09-08. Selective boundary condition reduction via learned error gating. https://arxiv.org/abs/2609.08461

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