18 citations · 64 across the 10 of their papers we have counts for
10 papers
Detecting Stochastic Governing Laws with Observation on Stationary Distributions
Xiaoli Chen, Hui Wang, Jinqiao Duan
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with obser…
An Onsager-Machlup approach to the most probable transition pathway for a genetic regulatory network
Jianyu Hu, Xiaoli Chen, Jinqiao Duan
We investigate a quantitative network of gene expression dynamics describing the competence development in Bacillus subtilis. First, we introduce an Onsager-Machlup approach to qua…
An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps
Wei Wei, Ting Gao, Jinqiao Duan +1
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian…
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…
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks
Xiaoli Chen, Liu Yang, Jinqiao Duan +1
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficient…
Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements
Xiaoli Chen, Jinqiao Duan, George Em Karniadakis
Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the so…