Di Qi  |  祁 迪

Curriculum Vitae

Research

Teaching

Publications



Contact:

Room 644
Department of Mathematics
Purdue University
150 N University St
West Lafayette, IN 47907


Email:

qidi at purdue dot edu

Currently an Assistant Professor at the Department of Mathematics, Purdue University. I'm interested in the general area of applied and computational mathematics, where mathematical tools and numerical methods are developed to address problems in science and engineering.

My current research topics mainly focus on numerical methods for PDEs, stochastic and statistical analysis, and uncertainty quantification. I'm working on model reduction strategies, statistical control methods, statistical stability analysis, turbulent diffusion, and data assimilation for complex turbulent dynamical systems, including their applications in fluid dynamics, atmosphere-ocean science, and plasma physics. For more details, see my research projects and publication list.

Research Opportunities: I have research problems available for graduate and undergraduate students who are interested in data-driven modeling and numerical method. Opportunities include funding for a student who would like to study mathematical problems at the interface of climate science, statistical physics, and geophysical fluid dynamics. Interested Purdue student should send me an e-mail so we can set up an appointment to chat about your background and interests.

Professional Appointments arrow right


Education &   Qualifications arrow right

  • 2017 - 2021   Postdoctoral Fellow, Courant Institute of Mathematical Sciences, New York University,   Mentor: Andrew J. Majda.

    • 2017   Ph.D. in Mathematics/Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University
    •     Advisor: Andrew J. Majda
    • 2012    B.S. in Mathematics (major) and Physics (minor), Shanghai Jiao Tong University, China.
    •      Advisor: Shi Jin

Teaching & Course information arrow right

Publications & Preprints arrow right

  • Qi, D.*, and Vanden-Eijnden, E., "Anomalous Statistics and Large Deviations of Turbulent Water Waves past a Step.", accepted, AIP Advancesarxiv:2112.09084, 2022 [.pdf]
  • Qi, D.*, and Harlim, J., " Machine Learning-Based Statistical Closure Models for Turbulent Dynamical Systems.", accepted, Philosophical Transactions A., arxiv:2108.13220, 2021 [.pdf]
  • Qi, D.*, "Unambiguous Models and Machine Learning Strategies for Anomalous Extreme Events in Turbulent Dynamical Systems.", submitted, Journal of Computational Physics., , 2021 [.pdf]
  • Qi, D.*, Majda, A.J. and Cerfon, A.J., "Dimits shift, avalanche-like bursts, and Solitary propagating structures in the two-field Flux-Balanced Hasegawa-Wakatani model for plasma edge turbulence (Featured article).", Physics of Plasmas, doi: 10.1063/5.0018943, 2020 [.pdf]
  • Qi, D.*, and Majda, A. J. "Nonlinear interaction and turbulence transition in the limiting regimes of plasma edge turbulence". Research in the Mathematical Sciences, 7(3), 1-32, 2020.
  • Moore, M.N.J., Bolles, C.T., Majda, A. J., and Qi, D., "Anomalous waves triggered by abrupt depth changes: Laboratory experiments and truncated KdV statistical mechanics.", Journal of Nonlinear Science, December 2020 [.pdf]
  • Qi, D.*, and Majda, A. J., "Flux-balanced two-field plasma edge turbulence in a channel geometry.", Physics of Plasmas, 2020 [.pdf]
  • Qi, D.*, and Majda, A. J., "Using machine learning to predict extreme events in complex systems.", Proceedings of the National Academy of Sciences, 2020 [.pdf]
  • Majda, A. J., and Qi, D.*, "Statistical phase transitions and extreme events in shallow water waves with an abrupt depth change.", Journal of Statistical Physics, 2019 [.pdf]
  • Majda, A. J., and Qi, D.*, "Linear and nonlinear statistical response theories with prototype applications to sensitivity analysis and statistical control of complex turbulent dynamical systems.", CHAOS: An Interdisciplinary Journal of Nonlinear Science, 2019 [.pdf]
  • Qi, D.*, Majda, A.J., and Cerfon, A.J., "A flux-balanced model for collisional plasma edge turbulence: numerical simulations with different aspect ratios.", Physics of Plasmas, 2019 [.pdf]
  • Qi, D.*, Majda, A.J., and Cerfon, A.J., "Linking the two-field dynamics of plasma edge turbulence with the one-field balanced model through systematic unstable forcing at low resistivity.", Physics of Plasmas, 2019 [.pdf]
  • Qi, D.* and Majda, A.J., "Zonal jet creation from secondary instability of drift waves for plasma edge turbulence", Chin. Ann. Math., arXiv:1901.08590, December 2018 [.pdf]
  • Majda, A.J., Moore, M.N.J., and Qi, D.*, "A statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change", Proc. Natl. Acad. Sci., December 2018 [.pdf]
  • Qi, D.*, Majda, A.J., and Cerfon, A.J., "A flux-balanced model for collisional plasma edge turbulence: numerical simulations with different aspect ratios", Physics of Plasmas, arXiv:1812.00131, November 2018 [.pdf]
  • Qi, D.* and Majda, A.J., "Transient metastability and selective decay for the coherent zonal structures in plasma edge turbulence", submitted, J. Nonlinear Sci., September 2018 [.pdf]
  • Majda, A.J. and Qi, D.*, "Using statistical functionals for effective control of inhomogeneous complex turbulent dynamical systems", Physica D: Nonlinear Phenomena, doi: 10.1016/j.physd.2018.12.003, December 2018 [.pdf]
  • Qi, D.* and Majda, A.J., "Rigorous statistical bounds in uncertainty quantification for one-layer turbulent geophysical flows", J. Nonlinear Sci., 28(5), pp. 1709–1761, doi: 10.1007/s00332-018-9462-1, October 2018 [.pdf]
  • Majda, A.J., Qi, D., and Cerfon, A.J., "A flux-balanced fluid model for collisional plasma edge turbulence: model derivation and basic physical features", Physics of Plasmas, 25(10), p.102307, doi: 10.1063/1.5049389, September 2018 [.pdf]
  • Qi, D.* and Majda, A.J., "Predicting extreme events for passive scalar turbulence in two-layer baroclinic flows through reduced-order stochastic models", Comm. Math. Sci., 16(1), pp.17–51, doi: 10.4310/CMS.2018.v16, April 2018 [.pdf]
  • Majda, A.J. and Qi, D.*, "Strategies for reduced-order models for predicting the statistical responses and uncertainty quantification in complex turbulent dynamical systems", SIAM Review, 60(3), pp. 491–549, doi: 10.1137/16M1104664, July 2017 [.pdf]
  • Majda, A.J. and Qi, D.*, "Effective control of complex turbulent dynamical systems through statistical functionals", Proc. Natl. Acad. Sci., 114(22), pp. 5571–5576, doi: 10.1073/pnas.1704013114 , May 2017 [.pdf]
  • Lee, Y., Majda, A.J., and Qi, D., "Stochastic superparameterization and multiscale filtering of turbulent tracers", SIAM--Multiscale Model. Simul., 15(1), pp. 215–234, doi: 10.1137/16M1080239 , January 2017 [.pdf]
  • Qi, D.* and Majda, A.J., "Low-dimensional reduced-order models for statistical response and uncertainty quantification: barotropic turbulence with topography", Physica D: Nonlinear Phenomena, 343, pp. 7–27, doi: 10.1016/j.physd.2016.11.006 , November 2016 [.pdf]
  • Lee, Y., Majda, A.J., and Qi, D., "Preventing catastrophic filter divergence using adaptive additive inflation for baroclinic turbulence", Mon. Weather Rev., 145(2), pp. 669–682, doi: 10.1175/MWR-D-16-0121.1 , October 2016 [.pdf]
  • Qi, D.* and Majda, A.J., "Low-dimensional reduced-order models for statistical response and uncertainty quantification: two-layer baroclinic turbulence", J. Atmos. Sci., 73(12), pp. 4609–4639, doi: 10.1175/JAS-D-16-0192.1 , August 2016 [.pdf]
  • Majda, A.J. and Qi, D.*, "Improving prediction skill of imperfect turbulent models through statistical response and information theory", J. Nonlinear Sci., 26(1), pp. 233–285, doi: 10.1007/s00332-015-9274-5 , February 2016 [.pdf]
  • Qi, D.* and Majda, A.J., "Predicting fat-tailed intermittent probability distributions in passive scalar turbulence with imperfect models through empirical information theory", Comm. Math. Sci., 14(6), pp. 1687–1722, doi: 10.4310/CMS.2016.v14 , January 2016 [.pdf]
  • Qi, D.* and Majda, A.J., "Blended particle methods with adaptive subspaces for filtering turbulent dynamical systems", Physica D: Nonlinear Phenomena, 298, pp. 21–41, doi:10.1016/j.physd.2015.02.002 , April 2015 [.pdf]
  • Majda, A.J., Qi, D., and Sapsis, T.P., "Blended particle filters for large dimensional chaotic dynamical systems", Proc. Natl. Acad. Sci., 111(21), pp. 7511–7516, doi: 10.1073/pnas.1405675111, May 2014 [.pdf]
  • (∗ indicates the corresponding author)

Conferences & Talks arrow right

Awards & Fellowships arrow right

  • 2017 Kurt O. Friedrichs prize for an outstanding dissertation in mathematics, New York University.
  • 2012 -- 2017 New York University MacCracken Graduate Scholarship, New York University.