I am a tenure-track assistant professor at Department of Mathematics. Before joining UCSB, I was a member of Prof. Mauro Maggioni's research group and worked as assistant research professor at Johns Hopkins University. Here is my CV. I am interested in solving problems in the mathematical foundations of Data Science. My current research projects are motivated by the need to exploit dynamical data sets in complex physical systems to perform inference with provable performance and build generalizable and interpretable predictive models, where I used and developed techniques from Statistical/Machine Learning, Harmonic Analysis, Approximation Theory, and Probability. My research can be categorized to the following two areas:

- Mathematical foundation of learning theory: statistical learning theory, statistical inference for ODEs,SDEs and PDEs from time-series data, high dimensional data analysis
- Applied and computational harmonic Analysis: functional analysis, Fourier analysis, approximation theory, sampling and frame theory, inverse problem in mathematical/statistical signal processing

**Postdoc position@UCSB:** : If you are interested in working with me,
please apply for the visiting assistant professor position at UCSB via
mathjobs and send me an email of your CV.

**RA position(for both undergraduate and graduate)@UCSB:** : If you are interested in exploring mathematics of cutting edge AI, please send me an email of your CV and transcript. The prerequisite are Math 201ABC or PSTAT197ABC or PSTAT 207, and 231.

** Independent Study(for both undergraduate and graduate)@UCSB:** : I am interested in modern data science topics. If you have interest in exploring a topic by paper reading or book reading, please feel free to send me an email of your CV and transcript, including a description of what kind of topics you want to explore.

- Math 260H: Seminar in mathematical foundation of data science
- Math 104C: Numerical Analysis

- 2011-2016 Vanderbilt Univerity; Mathematics ; PhD; Advisor: Prof. Akram Aldroubi
- 2007-2011 Sun Yat-Sen University; Mathematics; B.S.

- Sparse identification of nonlocal interaction kernel in nonlinear gradient flow equations via partial inversion (with Jose A. Carrillo,Gissell Estrada-Rodriguez, and Laszlo Mikolas), 1-44, submitted. ArXiv:2402.06355
- Convolutional dynamical sampling and some new results (with Longxiu Huang, Martina Newman, Yuying, Xie), 1-17, ArXiv:2406.15122
- On the Identifiablility of Nonlocal Interaction Kernels in First-Order Systems of Interacting Particles on Riemannian Manifolds (with Malik Tuerkoen, and Hanming Zhou), 1-20, to appear at Siam journal on Applied Mathematics.
- Learning Transition Operators From Sparse Space-Time Samples (with Christian Kummerel and Mauro Maggioni),to appear at IEEE Transactions on Information Theory, 1-35.
- Robust recovery of bandlimited graph signals via randomized dynamical sampling (with Longxiu Huang and Deanna Needell). ArXiv:2109.14079,1-40, to appear at Information and Inference, a journal of IMA.
- Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures (with Charles Kulick,Jinchao Feng), 1-40,submitted. ArXiv:2311.00902. To appear at Special Issue ``Machine learning and dynamical systems", Physica D: Nonlinear Phenomena.
- Learning particle swarm models from data with Gaussian process (with Jinchao Feng, Charles Kulick, and Yunxiang Ren),1-46, To appear at Mathematics of Computation. A short version is accepted as a poster presentation at Neurips Workshop 2021 Machine Learning and the Physical Sciences.
- Space-Time Variable Density Samplings for Sparse Bandlimited Graph Signals Driven by Diffusion Operators (with Qing Yao
**undergraduate student**and Longxiu Huang), to appear at IEEE ICASSP 2023, 1-5 - Higher-order error estimates for physics informed neural networks approximating primitive equations (with Ruimeng Hu, Quyuan Lin and Alan Rayden). 1-27, Partial Differential Equations and Applications, 34(4).
- A Interpretable Hybrid Predictive Model of COVID-19 Cases using Autoregressive Model and LSTM (with Yangyi Zhang
**undergraduate student**, and Guo Yu), 1-20, to appear at Scientific Reports, Nature Publishing Group. - Learning theory for inferring interaction kernels in second-order interacting agent Systems (with J. Miller, M. Zhong and M. Maggioni),1-55, To appear on special issue ''Data science, approximation, and harmonic analysis", Journal of Sampling Theory, Signal Processing, and Data Analysis, 2023.
- Scalable marginalization of latent variables for correlated data with applications to learning particle interaction kernels, (with Mengyang Gu, Xubo Liu, Xinyi Fang), 1-15, to appear at The New England Journal of Statistics in Data Science, 2022
- A Numerical Study on Sparse Learning of Interaction Laws in Homogeneous Multiparticle Systems with (
**Hao-Tien Chuang, Dongyang Li, Shelby Malowney, and Ritwik Trehan,undergraduate students**), SIAM Undergraduate Research Online, 232-249,2022. Code. - Estimate the spectrum of affine dynamical systems from partial
observations of a single trajectory data (with Jiahui Cheng,
**undergraduate student**). To appear at Inverse Problems, 1-43,2022. Code - Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories (with F. Lu and M. Maggioni). To appear at Foundations of Computational Mathematics, 1-55, 2021.
- Learning interaction kernels in heterogeneous systems of agents from multiple trajectories (with F. Lu and M. Maggioni). Journal of Machine Learning Research, 22 (32), 1-67, 2021. Code.
- On the identifiability of interaction functions in systems of interacting particles (with Z. Li, F. Lu, M. Maggioni and C. Zhang). Stochastic processes and their applications, Vol 132, 135 - 163, 2021.
- Sensor Calibration for Spectral Estimation Off the Grid (with Y. Eldar and W. Liao). Applied and Computational Harmonic Analysis,48(2), 570-598, 2020.
- Phaseless reconstruction from space-time samples (with A. Aldroubi and I. Krishtal). Applied and Computational Harmonic Analysis, 48(1), 395-414, 2020.
- Nonparametric inference of interaction laws in systems of agents from trajectory data (with F. Lu, M. Zhong and M. Maggioni). Proceedings of the National Academy of Sciences of USA, 116(29): 14424-14433, 2019. Appendix: 27 pages.
- Analysis of simulated crowd flow exit data: visualization, panic detection, exit time convergence, attribution and estimation (with A. Grim, B. Iskra, N. Ju, A. Kryshchenko, F.P. Medina, L. Ness, M. Ngamini, M. Owen, R. Paffenroth), Research in Data Science, 17:239-281, 2019.
- Undersampled windowed exponentials, spectra of Toeplitz operators and its applications (with C. Lai). Acta Applicanda Mathematicae, 164(1), 65-81, 2019
- Universal spatial-temporal sampling sets for discrete spatially invariant evolution systems. IEEE Transactions on Information Theory, 63(9): 5518-5528, 2017.
- System Identification in Dynamical Sampling. Advance in Computational Mathematics, 43(3): 555-580, 2017.
- Dynamical Sampling (with A. Aldroubi, C. Cabrelli and U. Molter). Applied and Computational Harmonic Analysis, 42(3): 378-401, 2017.
- Phase retrieval of evolving signals from space-time samples (with A. Aldroubi and I. Krishtal). Proceeding of 12th international conference on Sampling Theory and Applications, 2017.
- Multidimensional Signal Recovery in Discrete Evolution Systems via Spatiotemporal Trade Off (with R. Aceska and A. Petrosyan). Sampling Theory in Signal and Image Processing, 14(2):153-169, 2015.
- Filter Recovery in Infinite Spatially Invariant Evolutionary Systems via Spatiotemporal Trade off. Proceeding of 11th international conference on Sampling Theory and Applications, 2015.
- Dynamical sampling of two-dimensional temporally-varying signals (with R. Aceska and A. Petrosyan). Proceeding of 11th international conference on Sampling Theory and Applications, 2015.
- Dynamical sampling in hybrid shift invariant spaces (with R. Aceska). Contemporary Mathematics, American Mathematics Society, Providence, 626:149-166, 2014.

- Conference on Advances in data science: theory, methods and computation. TAMU, Oct 2022
- Kinetic Equations: Recent Developments and Novel Applications, Banff workshop, Oaxaca, Nov 2022
- UC Berkeley Applied math seminar, Nov 2022
- Special session on Mathematics of information theory, 2022 Pacific Rim Mathematical Association Congress, Vancouver, Dec 2022
- AMS Special Session on Current Progress in Computational Biomedicine, joint meeting, Boston, Jan 2023
- "Topics on Neuroscience, Collective Migration and Parameter Estimation", Mathematical Institute at the University of Oxford, July 2023.
- International Council for Industrial and Applied Mathematics (ICIAM), Tokyo, Japan, Aug 2023
- Isaac Newton Institute workshop "Measures and Representations of Interactions", Cambridge, UK, Sep 2023.