Yanlai Chen's Homepage

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Biography: CV in PDF
Yanlai Chen received his B.S. degree in Mathematics from University of Science and Technology of China (USTC), in 2002, M.S. in Computer Science and Engineering from Department of Computer Science and Engineering , and Ph.D. in Mathematics from School of Mathematics, University of Minnesota, in 2007. Prof. Cockburn, Bernardo was his thesis advisor. He then worked as a Postdoctoral Researcher supervised by Prof. Hesthaven Jan and Prof. Maday, Yvon at Brown University. Dr. Chen joined Department of Mathematics, University of Massachusetts Dartmouth in August 2010, as an Assistant Professor in Mathematics. He was promoted to Associate Professor with tenure in September 2016, and to Full Professor in September 2021.

Dr. Chen's administrative experience includes serving as a (Co-)Graduate Program Director of the Engineering and Applied Science program since September 2020, and as a Co-Director of the Center for Scientific Computing and Data Science Research from January to July of 2022.

Outside of work and spending time with his family, Dr. Chen enjoys running and serving his communities including via roles of school council and board of trustees members. He finished Boston Marathon in 2023 with a time 3:04:41.

Research Interest:

  • Numerical Analysis, Scientific Computing, Computational Partial Differential Equations
  • Dimension reduction, Data mining, Machine Learning, Data visualization
  • Neural networks, Meta learning
  • Conservation Laws, Hamilton-Jacobi-like equations and applications
  • Finite Element Discontinuous Galerkin Method, Adaptive numerical methods
  • Reduced Basis Methods, Reduced Basis Element Methods and Applications
  • Computational Electromagnetism
  • Mixed Finite Element Methods, Hybridizable Discontinuous Galerkin Methods
  • Uncertainty quantification, Fractional-order partial differential equations

  • The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Massachusetts, Dartmouth.


    Research supported by

    • National Science Foundation (DMS-1216928, DMS-1719698, DUE-2030552, DMS-2208277)
    • AFOSR (FA9550-18-1-0383), PI Gottlieb
    • UMass Dartmouth MUST program, established by Dr. Ramprasad Balasubramanian , sponsored by ONR (2020 - 2023), PI Heryudono
    • UMass Dartmouth Chancellor's Research Fund and Joseph P. Healey Endowment Grants (2011 - 2012)
    • A startup fund from college of arts and science (2010 - 2013)
    • UMassD multidisciplinary seed funding program (Spring 2014)
    • UMass President's office Science and Technology initiative funds (2013 - 2014)

    Related Profiles


    Major related links


    Navigating this page


    Helpful advices and tips

    • Advice for and Expectations from New and Current Students: Modest Advice from Dorsa Amir (HTML PDF);   Advice from Dr. Jan Hesthaven (HTML PDF)
    • A detailed checklist for paper writing (prepared by Dr. Zheng Zhang from UCSB). HTML   PDF

    Manuscripts submitted


    Title Author arXiv/Preprint
    A reduced basis warm-start iterative solver for the parameterized linear system S. Hou
    Y. Chen
    Y. Xia
    arXiv: 2311.13862
    MCMS-RBM: Multi-Component Multi-State Reduced Basis Method toward Efficient Transition Pathway Identification for Crystals and Quasicrystals Y. Ji
    L. Ji
    Y. Chen
    Z. Xu
    arXiv: 2308.15195


    Some journals in my field





    Published articles


    Title Author Journal DOI / arXiv
    A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation Z. Peng
    Y. Chen
    Y. Cheng
    F. Li
    arXiv: 2211.04677
    GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs Y. Chen
    S. Koohy
    Finite Elements in Analysis and Design arXiv: 2303.14878 DOI 10.1016/j.finel.2023.104047
    A fully conservative discontinuous Galerkin method via implicit penalization for the generalized KdV equation Y. Chen
    B. Dong
    R. Pereira
    SIAM J. Num. Anal. arXiv: 2211.05893
    DOI 10.1137/22M1470827
    Fast L2 optimal mass transport via reduced basis methods for the Monge-Ampere equation S. Hou
    Y. Chen
    Y. Xia
    SIAM J. Sci. Comput. arXiv: 2112.01878
    DOI 10.1137/21M1463720
    A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations Y. Chen
    L. Ji
    Z. Wang
    J. Comput. Phys. arXiv: 2110.11179
    DOI 10.1016/j.jcp.2022.111412
    A reduced basis method for radiative transfer equation Z. Peng
    Y. Chen
    Y. Cheng
    F. Li
    J. Sci. Comput. arXiv: 2103.07574
    DOI 10.1007/s10915-022-01782-2
    An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation Y. Chen
    S. Gottlieb
    L. Ji
    Y. Maday
    J. Comput. Phys. arXiv: 2101.05902
    DOI 10.1016/j.jcp.2021.110545
    L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations Y. Chen
    L. Ji
    A. Narayan
    Z. Xu
    J. Sci. Comput. arXiv: 2009.04812
    DOI 10.1007/s10915-021-01416-z
    Model reduction for fractional elliptic problems using Kato's formula H. Dinh
    H. Antil
    Y. Chen
    E. Cherkaev
    A. Narayan
    Math. Control Relat. Fields, To Appear arXiv: 1904.09332
    DOI 10.3934/mcrf.2021004
    Adaptive greedy algorithms based on parameter-domain decomposition and reconstruction for the reduced basis method J. Jiang
    Y. Chen
    Internat. J. Numer. Methods Engrg. To Appear arXiv: 1911.02214
    DOI 10.1002/nme.6544
    Certified reduced basis methods for fractional Laplace equations via extension H. Antil
    Y. Chen
    A. Narayan
    SIAM J. Sci. Comput. arXiv: 1808.00584
    DOI 10.1137/18M1204802
    Certified offline-free reduced basis (COFRB) methods for stochastic differential equations driven by arbitrary types of noise Y. Liu
    T. Chen
    Y. Chen
    C.-W. Shu
    J. Sci. Comput., To Appear Preprint
    DOI 10.1007/s10915-019-00976-5
    A reduced basis method for the nonlinear Poisson-Boltzmann equation L. Ji
    Y. Chen
    Z. Xu
    Advances in Applied Mathematics and Mechanics, To Appear. arXiv: 1808.09392
    DOI 10.4208/aamm.OA-2018-0188
    A robust error estimator and a residual-free error indicator for reduced basis methods Y. Chen
    J. Jiang
    A. Narayan
    Computers and Mathematics with Applications, To Appear. arXiv: 1710.08999
    DOI 10.1016/j.camwa.2018.11.032
    A Foreword to the Special Issue in Honor of Professor Bernardo Cockburn on His 60th Birthday: A Life Time of Discontinuous Schemings Y. Chen
    B. Dong
    C.-W. Shu
    Foreword to a special issue
    J. Sci. Comput.
    DOI 10.1007/s10915-018-0845-0
    A Hybridizable discontinuous Galerkin method for the Fifth-order Korteweg de-Vries equation B. Dong
    J. Jiang
    Y. Chen
    ESAIM: M2AN arXiv: 1710.07734
    DOI 10.1051/m2an/2018037
    Offline-Enhanced Reduced Basis Method through adaptive construction of the Surrogate Training Set J. Jiang
    Y. Chen
    A. Narayan
    J. Sci. Comput.
    (to appear) (2017)
    arXiv: 1703.05683
    DOI 10.1007/s10915-017-0551-3
    A goal-oriented RBM-Accelerated generalized polynomial chaos algorithm J. Jiang
    Y. Chen
    A. Narayan
    SIAM/ASA JUQ
    4 (2016), no. 1, 1398 -- 1420.
    arXiv Preprint
    JUQ Link
    A new discontinuous Galerkin method, conserving the discrete H2-norm, for third-order linear equations in one space dimension Y. Chen
    B. Cockburn
    B. Dong
    IMA J Numer Anal
    (2016) 36 (4): 1570 - 1598.
    doi: 10.1093/imanum/drv070
    A Certified Natural-Norm Successive Constraint Method for Parametric Inf-Sup Lower Bounds Y. Chen Applied Numer. Math.
    99 (2016) 98 - 108.
    doi: 10.1016/j.apnum.2015.09.003
    arXiv Preprint
    Reduced Basis Decomposition: a Certified and Fast Lossy Data Compression Algorithm Y. Chen Computers and Mathematics with Applications
    70 (2015) 2566 - 2574.
    doi: 10.1016/j.camwa.2015.09.023
    Corresponding downloadable software page.  
    arXiv Preprint
    [Refereed Proceedings] Using Visualization and Analysis with Efficient Dimension Reduction to Determine Underlying Factors in Hospital Inpatient Procedure Costs M. Perkins
    Y. Chen
    2015 IEEE Conference on Visual Analytics Science and Technology (VAST)
    vol. 00, pp. 205-206, 2015
    doi:10.1109/VAST.2015.7347680
    PDF at IEEExplore
    Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension Y. Chen
    B. Cockburn
    B. Dong
    Math. Comp.
    85 (2016), 2715 - 2742.
    Link
    A reduced radial basis function method for partial differential equations on irregular domains Y. Chen
    S. Gottlieb
    A. Heryudono
    A. Narayan
    J. Sci. Comput.
    (2016) 66(1):67 - 90.
    Link
    arXiv Preprint
    Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods Y. Chen
    S. Gottlieb
    Y. Maday
    C. R. Acad. Sci. Paris, Ser. I
    352 (2014) 661 - 666.
    doi: 10.1016/j.crma.2014.06.001
    arXiv Preprint
    Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes Y. Chen
    B. Cockburn
    Math. Comp.
    (2014) 83 (285) 87 - 111.
    Link
    [Education Journal] Transformation of a Mathematics Department's Teaching and Research Through a Focus on Computational Science Y. Chen
    G. Davis
    S. Gottlieb
    A. Hausknecht
    A. Heryudono
    S. Kim
    Journal of Computational Science Education
    (2013) 4(1), pp. 24-29.
    PDF
    Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework Y. Chen
    S. Gottlieb
    Journal of Scientific Computing
    55/3 (2013), pp. 718-737
    Link
    arXiv Preprint
    Certified Reduced Basis Method for Electromagnetic Scattering and Radar Cross Section Estimation Y. Chen
    J.S. Hesthaven
    Y. Maday
    J. Rodriguez
    Xueyu Zhu
    CMAME
    233 (2012) 92 - 108.
    doi: 10.1016/j.cma.2012.04.013
    Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part I: General nonconforming meshes Y. Chen
    B. Cockburn
    IMA J Numer Anal
    (2012) 32 (4): 1267 - 1293.
    doi: 10.1093/imanum/drr058
    A Seamless Reduced Basis Element Method for 2D Maxwell's Problem: An Introduction Y. Chen
    J.S. Hesthaven
    Y. Maday
    In Spectral and High Order Methods for Partial Differential Equations-Selected papers from the ICASOHOM'09 conference, J Hesthaven and EM Ronquist (eds). 2011, Volume 76, 141-152. Link  
    Updated Preprint
    A Natural-Norm Successive Constraint Method for Inf-Sup Lower Bounds D.B.P. Huynh
    D.J. Knezevic
    Y. Chen
    J.S. Hesthaven
    A.T. Patera
    CMAME
    199 (2010) 1963 - 1975
    doi: 10.1016/j.cma.2010.02.011
    Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations Y. Chen
    J.S. Hesthaven
    Y. Maday
    J. Rodriguez
    SISC
    32/2 (2010), pp. 970 - 996
    doi: 10.1137/09075250X
    Updated Preprint
    Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwell's Problem Y. Chen
    J.S. Hesthaven
    Y. Maday
    J. Rodriguez
    ESAIM: M2AN
    43 (2009) 1099 - 1116
    doi: 10.1051/m2an/2009037
    A Monotonic Evaluation of Lower Bounds for Inf-Sup Stability Constants in the Frame of Reduced Basis Approximations Y. Chen
    J. S. Hesthaven
    Y. Maday
    J. Rodriguez
    C. R. Acad. Sci. Paris, Ser. I
    346 (2008) 1295 - 1300.
    doi: 10.1016/j.crma.2008.10.012
    Preprint
    An adaptive high order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. Part I: the one dimensional steady state case Y. Chen
    B. Cockburn
    J. Comput. Phys.
    v 226/1(2007), pp. 1027-1058
    doi: 10.1016/j.jcp.2007.05.003



    Other Preprints


    Title Author arXiv/Preprint
    L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations Y. Chen
    S. Gottlieb
    L. Ji
    Y. Maday
    Z. Xu
    arXiv: 1906.07349
    Reduced-basis method for the iterative solution of parametrized symmetric positive-definite linear systems N. C. Nguyen
    Y. Chen
    arXiv: 1804.06363

    Research supported by

    • National Science Foundation (DMS-1216928, DMS-1719698, DUE-2030552, DMS-2208277)
    • AFOSR (FA9550-18-1-0383), PI Gottlieb
    • UMass Dartmouth MUST program, established by Dr. Ramprasad Balasubramanian , sponsored by ONR (2020 - 2023), PI Heryudono
    • UMass Dartmouth Chancellor's Research Fund and Joseph P. Healey Endowment Grants (2011 - 2012)
    • A startup fund from college of arts and science (2010 - 2013)
    • UMassD multidisciplinary seed funding program (Spring 2014)
    • UMass President's office Science and Technology initiative funds (2013 - 2014)

    Software Packages:

    • The Python package GPT-PINN. See here for the paper on ResearchGate.

      A NA G-ROMs talk given on 5/16/2023 on GPT-PINN:
    • A user-friendly page containing the Matlab test code using Reduced Basis Decomposition (RBD) for data compression (see paper   Reduced Basis Decomposition: a Certified and Fast Lossy Data Compression Algorithm.): Reduced Basis Decomposition page.

    • Sample applications of RBD
      • Lossy image compression and greedy face recognition FR_RBD page.

    • The suite of Matlab code for the reduced collocation method (see paper   Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework.) is available for download at RCM Software Page

    Research talks (Video):

    Misc. Slides:

    • Spring 2012 open house lecture at UMass Dartmouth is available here.
    • Spring 2014 open house lecture at UMass Dartmouth is available here.


    Office Location: LARTS 394A
    Phone Number: x8438

    Dedication to teaching and advising

    • Thanks to National Science Foundation, via grant DUE-2030552, we have established the ACCOMPLISH whose mission is to provide a multi-faceted financial and social support and contextualized computing-centered educational framework for eligible STEM students to propel them into the nation's high-quality STEM workforce.

    Navigating this page


    My schedule


    Current Teaching

    • See UMassD myCourses for the class webpages.


    Sample video of my in-class lectures (Fall 2019)


    Resources for Deep Learning


    Past Teaching


      Students

      Current Graduate Students

      David Gillcrist

      David is a PhD student who started in Fall 2020, jointly advised with Mazdak Tootkaboni from Civil Engineering

       Gillcrist

      Matthew Cormier

      Jointly advised with Sigal Gottlieb , Matt is a PhD student who started in Fall 2019. In Summer 2019, he started studying the mathematics for Neural Networks, in particular its utilities in time marching schemes.

       Cormier

      Haolan Zheng

      Haolan a PhD student who started in Fall 2023.

       Zheng

      Current Visiting/Oversea Doctoral Students

      Shijin Hou

      Shijin is a Doctoral student at the University of Science and Technology of China jointly advised with Yinhua Xia

      .
       Hou

      Yajie Ji

      Yajie is a Doctoral student at the Shanghai Jiaotong University jointly advised with Zhenli Xu

      .
       Ji

      Current Undergraduate Students

      Shawn Koohy

      Supported by an NSF grant, Shawn was a sophomore when he started exploring neural networks in Spring 2022.

       Koohy

      Alumni

      Rebecca Pereira

      Rebecca is a PhD student starting in Fall 2017. In Summer 2017, she worked on fast algorithms for geometric engineering design under uncertainty, jointly with Mazdak Tootkaboni from Civil Engineering. In Summer 2018, she started a project on (Hybridizable) discontinuous Galerkin method, jointly with Bo Dong from Mathematics.

      Upon graduation in Spring 2023, Rebecca started working at a federal agency

       Pereira

      Richard Bellizzi

      With Alfa Heryudono being the main advisor, Richard is a part-time PhD student and an employee at Nye Lubricants.

      Richard is currently working on building mathematical models and implementing machine learning algorithms for lubricant manufacturing.

      Upon graduation in Spring 2023, Richard has been continuing his career in the lubricant industry.

       Bellizzi

      Lijie Ji

      Lijie was a Doctoral student at the Shanghai Jiaotong University jointly advised with Zhenli Xu . She has been working on reduced basis method and reduced over collocation method since early 2018, and visited the CHEN lab from September 2019 to September 2020.

      Upon graduation in 2021, Lijie worked as a Wu Wen-Tsun Assistant Professor at the Shanghai Jiaotong University

       Lijie

      Jiahua Jiang

      Co-advised with Akil Narayan and working also under the guidance of Bo Dong , Jiahua focused on uncertainty quantification, and model order reduction. She started her doctoral study in Fall 2013, and graduated in Summer 2018.

      Jiahua's research has been supported by a fellowship from the Center for Scientific Computing and Visualization Research at UMassD, an NSF grant, and a UMassD Multi-disciplinary seed fund (MSF).

      Jiahua worked as a PostDoc at Virginia Tech University upon graduation in 2018, and is now an assistant professor at the University of Birmingham.

       Jiang

      Christopher Bresten

      Co-advised with Sigal Gottlieb and graduated in 2017, Chris was a PhD student working on model order reduction for nonlinear and nonaffine problems. He started this project in Fall 2012.

      Chris's research has been supported in part by an NSF grant.

      Chris is currently a PostDoc in Korea.

       Bresten

      Undergraduate Student alumni

      Chase Parenteau

      Chase is a honors student admitted to the university in 2018. He worked on mathematical models and machine learning algorithms for sports analytics in Spring 2019 and beyond.

       Parenteau

      Jonathan Curtis

      Jonathan is analyzing and implementing GPU-accelerated Reduced Basis Method. He started in Summer 2017.

      Jonathan's research has been supported by the department of mathematics, UMassD.

      Jonathan

      Ian Camerlin

      Ian is implementing GPU algorithms. He started in Summer 2014.

      Ian's research has been supported by an NSF grant. Ian graduated in 2016 and took a job in industry.

      Ian

      Peter Takahashi

      Peter started in Summer 2014 working on reduced basis type of model reduction techniques for data science.

      Peter's research was partially supported by the President's S&T grant. Peter chose to pursue his interests in computer science starting from Fall 2015. He graduated in 2017 and is a graduate student at Yale University.

      Peter

      Jacob Sousa

      Advised by and working with Alfa Heryudono before Spring 2014, Jacob worked with me on modeling and its reduction for a computational biology project in Spring 2014.He is now an EAS PhD student at the University of Massachusetts Dartmouth.

      Jacob's research was supported by the UMassD Multi-disciplinary seed funding (MSF) program.

      Jacob

      Andrew Davey

      Andrew mainly focused on implementing successive constraint methods in the collocation framework and devising appropriate variants. He started in Summer 2012 and left in Summer 2014 being awarded a Ben L. Fryrear Fellowship in Computational Science to pursue his PhD degree at the Colorado School of Mines.

      Andrew's research was mainly supported by an NSF grant and also by UMassD's Multidisciplinary Seed Funding (MSF) program.

      See below for a brief OUR (Office of Undergraduate Research) interview of Andrew talking about his experience at UMassD.

      Davey

      Rushendra Kumar

      Rushendra was a summer intern in 2012 coming from Indian Institute of Technology, Bhubaneswar. He is now at Springforth Capital Advisors in the Bhubaneshwar Area of India.

      Kumar

    Quick Links

    This page is organized and occasionally maintained by Yanlai Chen. Some of the sources are gotton from the Internet. I thank very much the authors sharing them on the Web. If some of them are copyrighted, please notify me and I will remove them as soon as possible

    Mathematical Links


    MISC


    MATHEMATICS ORGANIZATIONS:


    MISC. MATHEMATICS ORGANIZATIONS:


    Worldwide Mathematical Links


    On technical stuff

  • F2PY - Fortran to Python interface generator
  • Wrapping C codes using f2py
  • OpenMP
  • MPI
  • MatlabMPI
  • Mesh Generation on the web(Courtesy of Lin)
  • C Programming(courtesy of Dave.)


  •  Last Updated On: 6/4/10

    Contact Information

    Yanlai Chen Office: LARTS Room 394A
    Department of Mathematics Phone: 1-508-999-8438
    University of Massachusetts, Dartmouth Fax: 1-508-910-6917
    285 Old Westport Road E-mail: first.last@umassd.edu
    North Dartmouth, MA 02747