| Abstract: |
| In this talk, 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. 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 hypocoercivity theory of the model equation. Our analysis also suits for the general collisional kinetic equation including the full Boltzmann. We will show a series of numerical tests for forward and inverse problems, also extend to uncertainty quantification problems, to demonstrate the efficiency and robustness of our approach. |
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