Journal article
Asymptotic-preserving neural networks for the semiconductor Boltzmann equation and its application on inverse problems
Journal of computational physics, Vol.523, 113669
02/15/2025
DOI: 10.1016/j.jcp.2024.113669
Abstract
In this paper, we develop the Asymptotic-Preserving Neural Networks (APNNs) approach to study the forward and inverse problem for the semiconductor Boltzmann equation. The goal of the neural network is to resolve the computational challenges of conventional numerical methods and multiple scales of the model. To guarantee the network can operate uniformly in different regimes, it is desirable to carry the Asymptotic-Preservation (AP) property in the learning process. In a micro-macro decomposition framework, we design such an AP formulation of loss function. The convergence analysis of both the loss function and its neural network is shown, based on the Universal Approximation Theorem and hypocoercivity theory of the model equation. We show a series of numerical tests for forward and inverse problems of both the semiconductor Boltzmann and the Boltzmann-Poisson system to validate the effectiveness of our proposed method, which addresses the significance of the AP property when dealing with inverse problems of multiscale Boltzmann equations especially when only sparse or partially observed data are available.
•Asymptotic-Preserving Neural Networks for the semiconductor Boltzmann equation.•Convergence analysis via Universal Approximation Theorem and hypocoercivity theory.•Validation of APNNs for forward problems of Boltzmann and Boltzmann-Poisson system.•Effectiveness for solving inverse problems with partially observed data.
Details
- Title: Subtitle
- Asymptotic-preserving neural networks for the semiconductor Boltzmann equation and its application on inverse problems
- Creators
- Liu LiuYating WangXueyu ZhuZhenyi Zhu
- Resource Type
- Journal article
- Publication Details
- Journal of computational physics, Vol.523, 113669
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.jcp.2024.113669
- ISSN
- 0021-9991
- eISSN
- 1090-2716
- Grant note
- National Key R&D Program of China Ministry of Science and Technology in China: 2021YFA1001200 Research Grants Council of Hong Kong, Early Career Scheme: 24301021 General Research Fund - Research Grants Council of Hong Kong from 2021-2023: 14303022, 14301423 National Natural Science Foundation of China: 12301559
L. Liu acknowledges the support by National Key R&D Program of China Ministry of Science and Technology in China (2021YFA1001200), Research Grants Council of Hong Kong, Early Career Scheme (24301021) and General Research Fund (14303022 & 14301423) funded by Research Grants Council of Hong Kong from 2021-2023. Y. Wang acknowledges the support by National Natural Science Foundation of China (12301559).
- Language
- English
- Date published
- 02/15/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984769629202771
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