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math.NA2025
Asymptotic-preserving semi-Lagrangian discontinuous Galerkin schemes for the Boltzmann equation
Xiaofeng Cai, Zhen Hao, Liu Liu +1
In this work, we present an asymptotic-preserving semi-Lagrangian discontinuous Galerkin scheme for the Boltzmann equation that effectively handles multi-scale transport phenomena.…
math.NA2025
Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation
Jiayu Wan, Liu Liu
In this paper, we construct an asymptotic-preserving neural networks (APNNs) [21] for the linearized Boltzmann equation in the acoustic scaling and with uncertain parameters. Utili…
math.NA2024
Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties
Juntao Huang, Liu Liu, Kunlun Qi +1
The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving cl…