Research
Research Interests
Data-driven discovery of systems driven by (stochastic) differential equations
Modelling of complex stochastic dynamics in compuational chemistry and biology
Generative model and its applications in high dimensional sampling, inverse problems
Analysis and design of numerical algorithms for Partial Differential Equations, Finite Element Method, discontinuous Galerkin method
Publications
Note: † means equal contribution
Preprints
Yanfang Liu, Yuan Chen, Dongbin Xiu, Guannan Zhang. A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems, (2024+), submitted. [arXiv]
Yuan Chen, Dongbin Xiu. Modeling Unknown Stochastic Dynamical System Subject to External Excitation, (2024+), submitted. [arXiv]
Yuan Chen, Xu Zhang. A High-order Immersed C0 Interior Penalty Method for Biharmonic Interface
Problems., (2024+), preprint.
Journal Publications
Yuan Chen, Dongbin Xiu and Xiangxiong Zhang. On Enforcing Non-negativity in Polynomial Approximations in High Dimensions, SIAM Journal on Scientific Computing, in press, (2025). [arXiv]
Zhongshu Xu, Yuan Chen, Dongbin Xiu. Chebyshev Feature Neural Network for Accurate Function Approximation, Journal of Machine Learning for Modeling and Computing, 5 (2025), 1-14. [pdf] [arXiv]
Yuan Chen, Dongbin Xiu. Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems, Applied Mathematics for Modern Challenges, 2 (2024), 348-364. [pdf] [arXiv]
Zhongshu Xu†, Yuan Chen†, Qifan Chen†, Dongbin Xiu. Modeling Unknown Stochastic Dynamical System via Autoencoder, Journal of Machine Learning for Modeling and Computing, 5 (2024), 87-112. [pdf] [arXiv]
Yuan Chen, Dongbin Xiu. Learning Stochastic Dynamical System via Flow Map Operator, Journal of Computational Physics, 508 (2024), 112984. [pdf] [Slides]
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]
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]
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]
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]
Yuan Chen, Xu Zhang. A P2-P1 Partially Penalized Immersed Finite Element Method for Stokes Interface Problem. International Journal of Numerical Analysis and Modeling, 18 (2021), no. 1, 120-141. [pdf]
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]
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]
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