Research

Research Interests

• Data-driven modeling of systems driven by (stochastic) differential equations

• Numerical simulation of stochastic differential equations and rare events

• Finite Element Method, discontinuous Galerkin method, Virtual Element Method

• Interface problems and coupling mathematical models arising from applications

Publications

Note: \(^{\dagger}\) means equal contribution

Preprints

1. Yanfang Liu, Yuan Chen, Dongbin Xiu, Guannan Zhang. A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems, (2024+), submitted. [arXiv]

2. Zhongshu Xu, Yuan Chen, Dongbin Xiu. Chebyshev Feature Neural Network for Accurate Function Approximation, (2024+), submitted. [arXiv]

3. Yuan Chen, Dongbin Xiu. Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems, (2024+), submitted. [arXiv]

4. Yuan Chen, Dongbin Xiu. Modeling Unknown Stochastic Dynamical System Subject to External Excitation, (2024+), submitted. [arXiv]

5. Yuan Chen, Dongbin Xiu and Xiangxiong Zhang. On Enforcing Non-negativity in Polynomial Approximations in High Dimensions, (2024+), submitted. [arXiv]

6. Yuan Chen, Xu Zhang. A High-order Immersed \(C^0\) Interior Penalty Method for Biharmonic Interface Problems., (2024+), preprint.

Journal Publications

1. Zhongshu Xu\(^{\dagger}\), Yuan Chen\(\boldsymbol{^{\dagger}}\), Qifan Chen\(^{\dagger}\), Dongbin Xiu. Modeling Unknown Stochastic Dynamical System via Autoencoder, Journal of Machine Learning for Modeling and Computing, 5 (2024), 87-112. [pdf] [arXiv]

2. Yuan Chen, Dongbin Xiu. Learning Stochastic Dynamical System via Flow Map Operator, Journal of Computational Physics, 508 (2024), 112984. [pdf] [Slides]

3. Yuan Chen, Yulong Xing. Optimal Error Estimates of Ultra-weak Discontinuous Galerkin Methods with Generalized Numerical Fluxes for Multi-dimensional Convection-Diffusion and Biharmonic Equations. Mathematics of Computation, 93 (2024), 2135-2183. [pdf]

4. Yuan Chen, Xu Zhang. Solving Navier-Stokes Interface Problems with Fixed and Moving Interfaces on Unfitted Meshes. Journal of Scientific Computing, 98 (2024), 19. [pdf]

5. Victor Churchill, Yuan Chen, Zhongshu Xu, and Dongbin Xiu. DNN Modeling of Partial Differential Equations with Incomplete Data. Journal of Computational Physics, 493 (2023), 112502. [pdf]

6. Yuan Chen, Songming Hou, and Xu Zhang. Semi and Fully Discrete Analysis for An Immersed Finite Element Method for Elastodynamic Interface Problems. Computers and Mathematics with Applications, 147 (2023), 92-110. [pdf]

7. Yuan Chen, Xu Zhang. A \(\mathcal{P}_2\)-\(\mathcal{P}_1\) Partially Penalized Immersed Finite Element Method for Stokes Interface Problem. International Journal of Numerical Analysis and Modeling, 18 (2021), no. 1, 120-141. [pdf]

8. Yuan Chen, Songming Hou and Xu Zhang. A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-domains and Triple Junction Points. Results in Applied Mathematics, 8 (2020), 100100. [pdf]

9. Yuan Chen, Songming Hou and Xu Zhang. An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points. Advances in Applied Mathematics and Mechanics, 11 (2019), no. 5, 1005-1021. [pdf]