Research

Preprints 

• Wall laws for viscous flows in 3D randomly rough pipes: optimal convergence rates and stochastic integrability

In collaboration with M. Higaki and J. Zhuge
submitted [arxiv]

• Provable In-Context Learning of Linear Systems and Linear Elliptic PDEs with Transformers

In collaboration with F. Cole, Riley O'Neil and Tianhao Zhang

submitted [arXiv], [Code]

• Accelerating Langevin sampling with birth-death

In collaboration with J. Lu and J. Nolen.

[arXiv]

Published Journal Papers

• Generative downscaling of PDE solvers with physics-guided diffusion models 

In collaboration with W. Xu

Journal of Scientific Computing  101 (2024)  [arXiv]

• Fully discretized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem

In collaboration with Z. Chen, J. Lu, X. Zhang 

Accepted by Mathematics of Computation  [arXiv]

• Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms 

In collaboration with Y. Yang

Neural Networks 180 (2024) [arXiv]

• On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem

In collaboration with  Z. Chen, J. Lu, X. Zhang 

SIAM J. Numer. Anal.  62 (2023)  [arXiv]

• Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics

In collaboration with Dejan Slepčev and Lihan Wang

Nonlinearity (2023) [arXiv]

• A Regularity Theory for Static Schr\"odinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces

In collaboration with  Z. Chen, J. Lu and Shengxuan Zhou

SIAM J. Math. Anal. 55 (2023)  [arXiv]

• Exponential-wrapped distributions on symmetric spaces

In collaboration with D. Li, E. Chevalier and D. Dunson

SIAM Journal on Mathematics of Data Science (SIMODS). 4 (2022) [arXiv]

• Solving multiscale steady radiative transfer equation using neural networks with uniform stability

In collaboration with L. Wang and W. Xu

Research in the Mathematical Sciences [arXiv] [Code]

• A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems

In collaboration with J. Lu

 Communications of the American Mathematical Society (CAMS) [arXiv]

• Continuum limit and preconditioned Langevin sampling of the path integral molecular dynamics

In collaboration with J. Lu and Z. Zhou

Journal of Computational Physics, 415 (2020) [Journal] [arXiv]

• Quantitative propagation of chaos in the bimolecular reaction-diffusion model

In collaboration with T-S. Lim and J. Nolen.

SIAM J. Math. Anal. 52 (2020) [Journal] [arXiv]

• Geometric ergodicity of Langevin dynamics with Coulomb interactions

 In collaboration with J. C. Mattingly.

Nonlinearity. 33 (2019) [Journal] [arXiv]

• Uniform-in-Time weak error analysis for stochastic gradient descent Algorithms via diffusion approximation

In collaboration with Y. Feng, T. Gao, L. Li  and  J-G. Liu.

Commun.Math.Sci.  [Journal] [arXiv]

• Exponential decay of R\'enyi divergence under Fokker-Planck equations

In collaboration with Y. Cao and J. Lu. 

J. Stat. Phys. 176 (2019) [Journal] [arXiv]

•  An operator splitting scheme for the fractional kinetic Fokker-Planck equation,  

In collaboration with M. H.  Duong.

 Discrete Contin. Dyn. Syst. Ser. A. 39 (2019) [Journal] [arXiv]

• On the rate of convergence of empirical measures in $\infty$-Wasserstein distance for unbounded density function

In collaboration with A. Liu  and  J-G. Liu.

Quarterly of Applied Mathematics, 77 (2019) [Journal]  [arxiv] 

• Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance

In collaboration with Y. Cao and J. Lu. 

J. Math. Phys.  60(2019), 052202 (33 pages) [Journal] [arxiv] 

• Scaling limit of the Stein variational gradient descent: the mean field regime,

In collaboration with J. Lu and J. Nolen.

 SIAM J. Math. Anal. 51(2019), 648-671. (24 pages) ,  [Journal] [arXiv]

• Gaussian approximations for probability measures on $\R^d$,

In collaboration with A.M. Stuart and H. Weber. 

 SIAM/ASA J. Uncertainty Quantification. 5(1), 1136-1165. (2017).  (30 pages)  [Journal] [arXiv]

• Gaussian approximation for transition paths in Brownian dynamics,

In collaboration with A.M. Stuart and H. Weber. 

SIAM J. Math. Anal., 49(2017), 3005–3047. (43 pages) [Journal] [arXiv]

• A Bayesian level set method for geometric inverse problems, 

In collaboration with  M.A. Iglesias and A.M. Stuart.

 Interfaces and Free Boundaries, 18(2016), 181-217. (36 pages) [Journal] [arXiv]

• The factorization method for inverse elastic scattering from periodic structures,

 In collaboration with G. Hu and B. Zhang.

 Inverse Problems, 29 (2013), 115005. (25 pages) [Journal]

Peer-Reviewed Conference Proceedings

• Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian distributions

In collaboration with F. Cole

ICLR 2024, [arxiv]

• Two-scale gradient descent ascent dynamics finds mixed Nash equilibria of continuous games: A mean-field perspective

ICML 2023 [arXiv]

• Transfer learning enhanced DeepONet for long-time prediction of evolution equations

In collaboration with L. Wang and W. Xu

accepted by The 37th AAAI conference on Artificial Intelligence (2023). [arXiv] [Code]

• On the Representation of Solutions to Elliptic PDEs in Barron Spaces

In collaboration with Z. Chen and J. Lu

The 35th Conference on Neural Information Processing Systems (NeurIPS) (2021)  (Spotlight presentation). [arXiv]

• A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations

In collaboration with J. Lu and M. Wang

34th Annual Conference on Learning Theory (COLT 2021)  [arXiv]

• A Universal Approximation Theorem of Deep Neural Networks for Expressing Distributions

In collaboration with  J. Lu

The 34th Conference on Neural Information Processing Systems (NeurIPS) (2020) [arXiv]

• A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth

In collaboration with Y. Lu , C. Ma,  J. Lu and L. Ying 

The 37th International Conference on Machine Learning (ICML) (2020) [arXiv]

Unpublished note

• On the Bernstein-Von Mises Theorem for High Dimensional Nonlinear Bayesian Inverse Problems

 [arXiv]

Other publications

• Asymptotic analysis and computations of probability measures, PhD thesis, University of Warwick, 2017

 [Link]