182 citations · 1.5k across the 227 of their papers we have counts for
19 papers · 1 filter
Nonparametric inference of stochastic differential equations based on the relative entropy rate
Min Dai, Jinqiao Duan, Jianyu Hu +1
The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering gover…
Neural network stochastic differential equation models with applications to financial data forecasting
Luxuan Yang, Ting Gao, Yubin Lu +2
In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic t…
Data-driven method to learn the most probable transition pathway and stochastic differential equations
Jianyu Hu, Dongfang Li, Jinqiao Duan +1
Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are…
The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems
Wei Wei, Jianyu Hu
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting part…
Extracting stochastic dynamical systems with -stable Lévy noise from data
Yang Li, Yubin Lu, Shengyuan Xu +1
With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the…
Bohmian Trajectories of the Time-oscillating Schrödinger Equations
Dandan Li, Jinqiao Duan, Li Lin +1
Bohmian mechanics is a non-relativistic quantum theory based on a particle approach. In this paper we study the Schrödinger equation with rapidly oscillating potential and the asso…
Kantorovich-Rubinstein Distance and Approximation for Non-local Fokker-Planck Equations
Ao Zhang, Jinqiao Duan
This work is devoted to studying complex dynamical systems under non-Gaussian fluctuations. We first estimate the Kantorovich-Rubinstein distance for solutions of non-local Fokker-…
Most Probable Transitions from Metastable to Oscillatory Regimes in a Carbon Cycle System
Wei Wei, Jianyu Hu, Jianyu Chen +1
Global climate changes are related to the ocean's store of carbon. We study a carbonate system of the upper ocean, which has metastable and oscillatory regimes, under small random…
Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas
Yubin Lu, Yang Li, Jinqiao Duan
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems fro…
Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems
Yang Li, Jinqiao Duan
Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous phy…
Learning the temporal evolution of multivariate densities via normalizing flows
Yubin Lu, Romit Maulik, Ting Gao +3
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporall…
Stochastic turbulence for Burgers equation driven by cylindrical Lévy process
Shenglan Yuan, Dirk Blömker, Jinqiao Duan
This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodi…
Homogenization of Dissipative Hamiltonian Systems under Lévy Fluctuations
Zibo Wang, Li Lv, Jinqiao Duan
This work is devoted to deriving small mass limiting equation for a class of Hamiltonian systems with multiplicative Lévy noise. Derivation of the limiting equation depends on the…
The Most Probable Transition Paths of Stochastic Dynamical Systems: A Sufficient and Necessary Characterization
Yuanfei Huang, Qiao Huang, Jinqiao Duan
The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not s…
Convergence rate for homogenization of a nonlocal model with oscillating coefficients
Li Lin, Jinqiao Duan
This letter deals with homogenization of a nonlocal model with Levy-type operator of rapidly oscillating coefficients. This nonlocal model describes mean residence time and other e…
Variational inference of the drift function for stochastic differential equations driven by Lévy processes
Min Dai, Jinqiao Duan, Jianyu Hu +1
In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by -stable Lévy motion. First, the Kullback-Lei…
Detection of bistable structures via the Conley index and applications to biological systems
Junbo Jia, Pan Yang, Huaiping Zhu +3
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in dynamical systems are studied: One is two one-point attractors, another…
Dynamical behavior of a nonlocal Fokker-Planck equation for a stochastic system with tempered stable noise
Li Lin, Jinqiao Duan, Xiao Wang +1
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fok…
Large Deviations for SDE driven by Heavy-tailed Lévy Processes
Wei Wei, Qiao Huang, Jinqiao Duan
We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed Lévy processes. These heavy-tailed Lévy…