31 citations · 31 across the 6 of their papers we have counts for
7 papers
Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise
Yang Li, Jinqiao Duan
Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths…
Noise-intensity bifurcations of transition paths by Morse index formula
Jinqiao Duan, Zhihao Zhao
We study most probable transition paths (MPTPs) of a gradient diffusion system in with fixed endpoints, in the framework of Onsager--Machlup (OM) theory. The existen…
Homogenization and corrector results for the stochastic non-homogeneous incompressible Navier-Stokes equations with rapid oscillation
Zhaoyang Qiu, Junlong Chen, Jinqiao Duan
In this paper we are concerned with the homogenization property of stochastic non-homogeneous incompressible Navier-Stokes equations with rapid oscillation in a smooth bounded doma…
An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas
Yang Li, Shengyuan Xu, Jinqiao Duan
Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise from data is chanllenging due to possible…
Stochastic parameter reduced-order model based on hybrid machine learning approaches
Cheng Fang, Jinqiao Duan
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation an…
Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient
Weiguo Lu, Xuan Wu, Deng Ding +3
Diffusion models (DMs) are a type of generative model that has a huge impact on image synthesis and beyond. They achieve state-of-the-art generation results in various generative t…
A Machine Learning Framework for Computing the Most Probable Paths of Stochastic Dynamical Systems
Yang Li, Jinqiao Duan, Xianbin Liu
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probabl…