7 citations · 9 across the 8 of their papers we have counts for
10 papers
Data-driven Effective Modeling of Stochastic Chemical Reaction Networks
Yuan Chen, Weize Mao, Dongbin Xiu
The Stochastic Simulation Algorithm (SSA), widely considered an exact algorithm for stochastic chemical reaction networks, suffers from high computational cost. In this work, we pr…
Modeling Unknown Nonlocal PDE Systems via Flow Map Learning
Zhongshu Xu, Ying Li, Yanzhi Zhang +1
Nonlocal partial differential equations arise in many applications but are often difficult to model and learn because of the presence of nonlocal operators. We present a flow-map l…
Targeted Digital Twin via Flow Map Learning and Its Application to Fluid Dynamics
Qifan Chen, Zhongshu Xu, Jinjin Zhang +1
We present a numerical framework for constructing a targeted digital twin (tDT) that directly models the dynamics of quantities of interest (QoIs) in a full digital twin (DT). The…
DUE: A Deep Learning Framework and Library for Modeling Unknown Equations
Junfeng Chen, Kailiang Wu, Dongbin Xiu
Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering discip…
A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems
Yanfang Liu, Yuan Chen, Dongbin Xiu +1
This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key chal…
Chebyshev Feature Neural Network for Accurate Function Approximation
Zhongshu Xu, Yuan Chen, Dongbin Xiu
We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure…
Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems
Yuan Chen, Dongbin Xiu
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unkn…
Modeling Unknown Stochastic Dynamical System Subject to External Excitation
Yuan Chen, Dongbin Xiu
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our b…
On enforcing non-negativity in polynomial approximations in high dimensions
Yuan Chen, Dongbin Xiu, Xiangxiong Zhang
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negat…
Modeling Unknown Stochastic Dynamical System via Autoencoder
Zhongshu Xu, Yuan Chen, Qifan Chen +1
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown…