Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation
Year: 2026
Type: article
Abstract: In this paper, we construct an asymptotic-preserving neural network (APNN) (Jin et al., J. Sci. Comput. 94 (2023) 57) for the linearized Boltzmann equation with uncertain parameters. Utilizing the micro-macro decomposition, we design the loss function based on the stochastic-Galerkin system conducted from the micro-macro equations. Rigorous analysis is provided to show the capability of the neural network in approximating solutions near the global Maxwellian. By employing hypocoercivity techniques, we demonstrate two key results: (i) the existence of APNN leading to arbitrarily small loss function, and (ii) the cor convergence of the APNN's approximated solution as the loss tends to zero, with the error exhibiting an exponential decay in time.
Authors: Jiayu Wan, Liu Liu, Zhenyi Zhu
Institution: Chinese University of Hong Kong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7110929053
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