Selective boundary condition reduction via learned error gating
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Abstract (arXiv)
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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References · 8
- 2017Selective Classification for Deep Neural Networkscited by 799
- 2016Distribution-Free Predictive Inference For Regressioncited by 657
- 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
- 2024Neural Operators with Localized Integral and Differential Kernelscited by 59
- 2022Mitigating spectral bias for the multiscale operator learningcited by 43
- 2022Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuitiescited by 29
- 2024Component Fourier Neural Operator for Singularly Perturbed Differential Equationscited by 7
- 2022Semi-analytic PINN methods for singularly perturbed boundary value problemscited by 6
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