arXiv subjects

Zichang Ju

Publications and source records attributed to Zichang Ju.

2 recordsLinked to original sources

arXiv2026

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

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.

math.NA↗

arXiv2025

A modified tamed scheme for stochastic differential equations with superlinear drifts

Explicit discretizations of stochastic differential equations often encounter instability when the coefficients are not globally Lipschitz. The truncated schemes and tamed schemes have been proposed to handle this difficulty, but truncated schemes involve analyzing of the stopping times while the tamed schemes suffer from the reduced order of accuracy. We propose a modified tamed scheme by introducing an additional cut-off function in the taming, which enjoys the convenience for error analysis and preserving the original order of explicit discretization. While the strategy could be applied to any explicit discretization, we perform rigorous analysis of the modified tamed scheme for the Euler discretization as an example. Then, we apply the modified tamed scheme to the stochastic gradient Langevin dynamics for sampling with super-linear drift, and obtain a uniform-in-time near-sharp error estimate under relative entropy.

math.NA↗