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arXiv · 2608.22880

A particle method for the Boltzmann equation via amortized sampling from Green's function of the lifted linear operator

Zichang Ju·Lei Li·Yang Yu
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Abstract

The collision operator for the Boltzmann equation is a nonlinear nonlocal operator. When lifted in the extended 2-particle space, it is viewed as the projection of a collisional linear operator. In this paper, we propose a particle method that samples the post-collision relative velocity directly from the Green's function of this operator (the transition probability of the generated time-continuous Markov chain). The normalizing flow amortized sampling is then proposed to reduce the sampling complexity. The resulted method takes $O(N)$ each time where $N$ is the particle number, and conserves momentum and energy exactly. This method does not require the boundedness of the kernel and, more importantly, it allows learning the Green's function directly from the scattering data without selecting the kernel in a specified family.

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Zichang Ju, Lei Li, Yang Yu. 2026-08-24. A particle method for the Boltzmann equation via amortized sampling from Green's function of the lifted linear operator. https://arxiv.org/abs/2608.22880

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