Preprint
A Bi-fidelity based asymptotic-preserving neural network for the semiconductor Boltzmann equation and its inverse problem
ArXiv.org
Cornell University
11/17/2025
DOI: 10.48550/arxiv.2511.13321
Abstract
This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Boltzmann equation. Our approach builds upon the Asymptotic-Preserving Neural Network (APNNs) methodology APNN-transport, which employs a micro-macro decomposition to handle the model's multiscale nature. We specifically address a key bottleneck in the original APNNs: the slow convergence of the macroscopic density$ρ$in the near fluid-dynamic regime, i.e., for small Knudsen numbers$\varepsilon$ . The core innovation of BI-APNNs is a novel bi-fidelity decomposition of the macroscopic quantity$ρ$ , which accurately approximates the true density at small$\varepsilon$ , and can be efficiently pre-trained. A separate and more compact neural network is then tasked with learning only the minor correction term,$ρ_{\text{corr}}$ . This strategy not only significantly ıt accelerates the training convergence but also improves the accuracy of the forward problem solution, particularly in the challenging fluid-dynamic limit. Meanwhile, we demonstrate through extensive numerical experiments that our new BI-APNNs yields substantially more accurate and robust results for inverse problems compared to the standard APNNs. Validated on both the semiconductor Boltzmann and the Boltzmann-Poisson systems, our work shows that the bi-fidelity formulation is a powerful enhancement for tackling multiscale kinetic equations, especially when dealing with inverse problems constrained by partial observation data.
Details
- Title: Subtitle
- A Bi-fidelity based asymptotic-preserving neural network for the semiconductor Boltzmann equation and its inverse problem
- Creators
- Liu LiuXueyu ZhuZhenyi Zhu
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2511.13321
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 11/17/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9985033871702771
Metrics
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