5 papers
Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds
Nathanael Tepakbong, Hanyu Hu, Chengyu Liu +1
Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-con…
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…
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…
Generating Samples of Stationary Distributions of Weakly Interacting Diffusion Models Without Finite Particle Truncation: A Weak Generative Approach
Zhiqiang Cai, Chengyu Liu, Xiang Zhou
Computing the stationary probability density and generating corresponding samples for the mean-field model of an infinite number of weakly interacting diffusion particles pose sign…