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math.NA2024
Lévy Score Function and Score-Based Particle Algorithm for Nonlinear Lévy--Fokker--Planck Equations
Yuanfei Huang, Chengyu Liu, Xiang Zhou
The score function for the diffusion process, also known as the gradient of the log-density, is a basic concept to characterize the probability flow with important applications in…
math.PR2024
Probability Flow Approach to the Onsager--Machlup Functional for Jump-Diffusion Processes
Yuanfei Huang, Xiang Zhou, Jinqiao Duan
The Onsager--Machlup action functional is an important concept in statistical mechanics and thermodynamics to describe the probability of fluctuations in nonequilibrium systems. It…
cs.LG2024
Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equation
Zhiqiang Cai, Yu Cao, Yuanfei Huang +1
Sampling invariant distributions from an Itô diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential…