6 papers
Generative Path-Finding Method for Wasserstein Gradient Flow
Chengyu Liu, Xiang Zhou
Wasserstein gradient flows (WGFs) describe the evolution of probability distributions in Wasserstein space as steepest descent dynamics for a free energy functional. Computing the…
Transition Path Theory For Lévy-Type Processes: SDE Representation and Statistics
Yuanfei Huang, Xiang Zhou
This paper establishes a Transition Path Theory (TPT) for Lévy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non…
Entropy Production in Non-Gaussian Active Matter: A Unified Fluctuation Theorem and Deep Learning Framework
Yuanfei Huang, Chengyu Liu, Bing Miao +1
We present a general framework for deriving entropy production rates (EPRs) in active matter systems driven by non-Gaussian active fluctuations. Employing the probability-flow equi…
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…
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…
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…