7 citations · 9 across the 8 of their papers we have counts for
5 papers · 1 filter
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…