Research
My research aims to develop rigorous foundations and algorithms for high-dimensional computational challenges in applied mathematics, statistics, and data science. These challenges are prevalent in fine-scale physical equations, large-scale machine learning datasets, and statistical/stochastic models with complex uncertainties. I am interested in formalizing and exploring the following high level questions:
- How to understand and achieve provably efficient numerical estimation for PDEs, matrices, and probability distributions, especially in high dimensional or heterogeneous settings?
- How to accelerate and automate these estimations with machine learning rigorously?
For specfic topics, please see the bottom of the About Page.
Publications
Preprints
Scale-Adaptive Generative Flows for Multiscale Scientific Data
Yifan Chen, Eric Vanden-Eijnden
Submitted, 2025. [arXiv] [Code]Lipschitz-Guided Design of Interpolation Schedules in Generative Models
Yifan Chen, Eric Vanden-Eijnden, Jiawei Xu
Submitted, 2025. [arXiv] [Code]Split Gibbs Discrete Diffusion Posterior Sampling
Wenda Chu, Zihui Wu, Yifan Chen, Yang Song, Yisong Yue
Submitted, 2025. [arXiv] [Code]New Affine Invariant Ensemble Samplers and Their Dimensional Scaling
Yifan Chen
Submitted, 2025. [arXiv] [Code] [Slide]Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias
Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed, Jonathan Weare
Submitted, 2024. [arXiv] [Slide]Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalities
José A. Carrillo, Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Dongyi Wei
Submitted, 2024. [arXiv]Sampling via Gradient Flows in the Space of Probability Measures
Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, Andrew M. Stuart
Submitted, 2023. [arXiv] [Code] [Slide]
Conference Publications
Probabilistic Forecasting with Stochastic Interpolants and Follmer Processes
Yifan Chen, Mark Goldstein, Mengjian Hua, Michael S. Albergo, Nicholas M. Boffi, Eric Vanden-Eijnden
ICML, 2024. [Proceedings] [arXiv] [Slide] [Code] [Poster]Inpainting crystal structure generations with score-based denoising
Xinzhe Dai, Peichen Zhong, Bowen Deng, Yifan Chen, Gerbrand Ceder
ICML Workshop AI4Science, 2024. [Proceedings]Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors
Zihui Wu, Yu Sun, Yifan Chen, Bingliang Zhang, Yisong Yue, Katherine L. Bouman
NeurIPS, 2024. [Proceedings] [arXiv] [Code]
Journal Publications
Sequential-in-time Training of Nonlinear Parametrizations for Solving Time-dependent Partial Differential Equations
Huan Zhang, Yifan Chen, Eric Vanden-Eijnden, Benjamin Peherstorfer
Accepted at SIAM Review Research Spotlights, 2025. [arXiv]Stable Derivative Free Gaussian Mixture Variational Inference for Bayesian Inverse Problems
Baojun Che, Yifan Chen, Zhenghao Huan, Daniel Zhengyu Huang, Weijie Wang
Accepted at SIAM Journal on Scientific Computing, 2025. [arXiv] [Code]Randomly Pivoted Cholesky: Practical Approximation of A Kernel Matrix with Few Entry Evaluations
Yifan Chen, Ethan N. Epperly, Joel A. Tropp, Robert J. Webber
Communications on Pure and Applied Mathematics, 2024. [Journal] [arXiv] [Code] [Slide]Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation
Yifan Chen, Bamdad Hosseini, Houman Owhadi, Andrew M. Stuart
Statistics and Computing, 2024. [Journal] [arXiv] [Code]Efficient, Multimodal, and Derivative-Free Bayesian Inference with Fisher-Rao Gradient Flows
Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, Andrew M. Stuart
Inverse Problems, 2024. [Journal] [arXiv] [Code] [Slide]Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
Pau Batlle, Yifan Chen, Bamdad Hosseini, Houman Owhadi, Andrew M. Stuart
Jounal of Computational Physics, 2024. [Journal] [arXiv] [Code]Provable Probabilistic Imaging using Score-Based Generative Priors
Yu Sun, Zihui Wu, Yifan Chen, Berthy T. Feng, Katherine L. Bouman
IEEE Transactions on Computational Imaging, 2024. [Journal] [arXiv] [Code]Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
Yifan Chen, Houman Owhadi, Florian Schaefer
Mathematics of Computation, 2024. [Journal] [arXiv] [Code] [Slide] [Slide+]Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations
Yifan Chen, Thomas Y. Hou, Yixuan Wang
SIAM Multiscale Modeling and Simulation, 2023. [Journal] [arXiv] [Slide] [Slide+]Exponentially Convergent Multiscale Finite Element Method
Yifan Chen, Thomas Y. Hou, Yixuan Wang
Communications on Applied Mathematics and Computation, 2023. [Journal] [arXiv] [Slide] [Slide+]Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data
Yifan Chen, Thomas Y. Hou
SIAM Multiscale Modeling and Simulation, 2022. [Journal] [arXiv] [Code]Solving and Learning Nonlinear PDEs with Gaussian Processes
Yifan Chen, Bamdad Hosseini, Houman Owhadi, Andrew M. Stuart
Jounal of Computational Physics, 2021. [Journal] [arXiv] [Code] [Slide] [Slide+]Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions
Yifan Chen, Thomas Y. Hou, Yixuan Wang
SIAM Multiscale Modeling and Simulation, 2021. [Journal] [arXiv] [Slide] [Slide+]Consistency of Empirical Bayes and Kernel Flow For Hierarchical Parameter Estimation
Yifan Chen, Houman Owhadi, Andrew M. Stuart
Mathematics of Computation, 2021. [Journal] [arXiv] [Code] [Slide] [Longer Slide] [Short Video] [Longer Video]Function Approximation via The Subsampled Poincare Inequality
Yifan Chen, Thomas Y. Hou
Discrete & Continuous Dynamical Systems - A, 2020. [Journal] [arXiv]Optimal Transport Natural Gradient for Statistical Manifolds with Continuous Sample Space
Yifan Chen, Wuchen Li
Information Geometry, 2020. [Journal] [arXiv] [Code] [Slide]Run-and-Inspect Method for Nonconvex Optimization and Global Optimality Bounds for R-Local Minimizers
Yifan Chen, Yuejiao Sun, Wotao Yin
Mathematical Programming, 2019. [Journal] [arXiv] [Slide]The Quadratic Wasserstein Metric for Earthquake Location
Jing Chen, Yifan Chen, Hao Wu, Dinghui Yang
Journal of Computational Physics, 2018. [Journal] [arXiv] [Slide]
Thesis
On Multiscale and Statistical Numerical Methods for PDEs and Inverse Problems
Yifan Chen
Ph.D. Thesis, The W.P. Carey and Co. Prize in Applied Mathematics, 2023 [CaltechTHESIS] [Slide]
Notes
Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, Andrew M. Stuart
[arXiv]
Professional Experience
Referee Service
- Reviewer for NeurIPS
- Reviewer for PNAS
- Reviewer for Nature Machine Intelligence
- Reviewer for Communications on Pure and Applied Mathematics
- Reviewer for Annals of Applied Probability
- Reviewer for Journal of Functional Analysis
- Reviewer for Journal of Machine Learning Research
- Reviewer for Mathematics of Computation
- Reviewer for Journal of Computational Physics
- Reviewer for SIAM on Uncertainty Quantification
- Reviewer for SIAM on Imaging Sciences
- Reviewer for SIAM on Optimization
- Reviewer for SIAM on Mathematics of Data Science
- Reviewer for SIAM on Multiscale Modeling and Simulation
- Reviewer for SIAM on Numerical Analysis
- Reviewer for SIAM on Control and Optimization
- Reviewer for IMA Journal of Numerical Analysis
- Reviewer for Linear Algebra and Its Applications
- Reviewer for European Journal of Applied Mathematics
- Reviewer for Foundations of Data Science
- Reviewer for Analysis and Applications
- Reviewer for Discrete and Continuous Dynamical Systems
- Reviewer for Research in the Mathematical Sciences
- Reviewer for Computers & Fluids
- Reviewer for Computational Methods in Applied Mathematics
- Reviewer for International Journal of Computer Mathematics
- Reviewer for 4th International Conference, GSI 2019