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math.NA2025
A Bi-fidelity based asymptotic-preserving neural network for the semiconductor Boltzmann equation and its inverse problem
Liu Liu, Xueyu Zhu, Zhenyi Zhu
This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Bolt…
math.NA2022★ 12 cited
Physics-informed neural networks for learning the homogenized coefficients of multiscale elliptic equations
Jun Sur Richard Park, Xueyu Zhu
Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). Th…