Research — Yuan Chen

Research Interests

Data-driven modeling of stochastic dynamics
Generative models and applications in scientific computing
Design and analysis of finite element method and discontinuous Galerkin method

Publications

\(^\dagger\) denotes equal contribution

Preprints

Data-driven Effective Modeling of Stochastic Chemical Reaction Networks PDF arXiv Code

Y. Chen, W. Mao, and D. Xiu, arXiv preprint, 2026.

Journal Publications

A High-order Immersed \(C^0\) Interior Penalty Method for Biharmonic Interface Problems PDF arXiv

Y. Chen and X. Zhang, Journal of Scientific Computing, 108 (2026), 38.
Modeling Unknown Stochastic Dynamical System Subject to External Excitation PDF arXiv Code

Y. Chen and D. Xiu, SIAM Journal on Scientific Computing (2026), no. 2, C216–C239.
A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems PDF arXiv Code

Y. Liu, Y. Chen, D. Xiu, and G. Zhang, SIAM Journal on Scientific Computing (2025), no. 5, C1144–C1171.
On Enforcing Non-negativity in Polynomial Approximations in High Dimensions PDF arXiv

Y. Chen, D. Xiu, and X. Zhang, SIAM Journal on Scientific Computing, 47 (2025), no. 2, A866–A888.
Chebyshev Feature Neural Network for Accurate Function Approximation PDF arXiv Code

Z. Xu, Y. Chen, and D. Xiu, Journal of Machine Learning for Modeling and Computing, 5 (2025), 1–14.
Optimal Error Estimates of Ultra-weak Discontinuous Galerkin Methods with Generalized Numerical Fluxes for Multi-dimensional Convection-Diffusion and Biharmonic Equations PDF

Y. Chen and Y. Xing, Mathematics of Computation, 93 (2024), 2135–2183.
Modeling Unknown Stochastic Dynamical System via Autoencoder PDF arXiv Code

Z. Xu\(^\dagger\), Y. Chen\(^\dagger\), Q. Chen\(^\dagger\), and D. Xiu, Journal of Machine Learning for Modeling and Computing, 5 (2024), 87–112.
Learning Stochastic Dynamical System via Flow Map Operator PDF arXiv Code

Y. Chen and D. Xiu, Journal of Computational Physics, 508 (2024), 112984.
Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems PDF arXiv Code

Y. Chen and D. Xiu, Applied Mathematics for Modern Challenges, 2 (2024), 348–364.
Solving Navier-Stokes Interface Problems with Fixed and Moving Interfaces on Unfitted Meshes PDF

Y. Chen and X. Zhang, Journal of Scientific Computing, 98 (2024), 19.
DNN Modeling of Partial Differential Equations with Incomplete Data PDF

V. Churchill, Y. Chen, Z. Xu, and D. Xiu, Journal of Computational Physics, 493 (2023), 112502.
Semi and Fully Discrete Analysis for An Immersed Finite Element Method for Elastodynamic Interface Problems PDF

Y. Chen, S. Hou, and X. Zhang, Computers and Mathematics with Applications, 147 (2023), 92–110.
A \(\mathcal{P}_2\)-\(\mathcal{P}_1\) Partially Penalized Immersed Finite Element Method for Stokes Interface Problem PDF

Y. Chen and X. Zhang, International Journal of Numerical Analysis and Modeling, 18 (2021), no. 1, 120–141.
A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-domains and Triple Junction Points PDF

Y. Chen, S. Hou, and X. Zhang, Results in Applied Mathematics, 8 (2020), 100100.
An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points PDF

Y. Chen, S. Hou, and X. Zhang, Advances in Applied Mathematics and Mechanics, 11 (2019), no. 5, 1005–1021.

Thesis

Data-driven Modeling of Stochastic Dynamical Systems PDF

Yuan Chen, Ph.D. Thesis, 2026.