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.

My research is supported by NSF DMS-2407361 and ONR N00014-24-1-2192.

Research Opportunities: I have research opportunities available for postdocs, graduate and undergraduate students who are interested in interdisciplinary research involving rigorous mathematical theories, numerical analysis, data-driven modeling and computational methods. Feel free to send me an e-mail and we can set up an appointment to chat about your interests.

Professional Appointments arrow right








Education &   Qualifications arrow right

  • 2021 - current   Assitant Professor, Department of Mathematics, Purdue University.
  •          Affiliate, Department of Earth, Atmospheric, and Planetary Sciences, Purdue University.
  • 2017 - 2021   Postdoctoral Fellow, Courant Institute of Mathematical Sciences, New York University.

    • 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 Liu, J.-G., "Oscillatory solutions at the continuum limit of Lorenz 96 systems", submitted arXiv preprint arXiv:2410.10073, 2025 [.pdf]
  • Mohamad, M.A., and Qi, D., "Modeling extreme events and intermittency in turbulent diffusion with a mean gradient", submitted arXiv preprint arXiv:2505.21688, 2025 [.pdf]
  • Qi, D.*, and Liu, J.-G., "Data assimilation models for computing probability distributions of complex multiscale systems", submitted arXiv preprint arXiv:2503.22949, 2025 [.pdf]
  • Wang, Z., Chen, N., and Qi, D., "A closed-form nonlinear data assimilation algorithm for multi-layer flow fields", submitted arXiv preprint arXiv:2412.11042, 2024 [.pdf]
  • Qi, D.*, and Liu, J.-G., "Coupled stochastic-statistical equations for filtering multiscale turbulent systems", submitted arXiv preprint arXiv:2407.04881, 2024 [.pdf]
  • Gao, Y., and Qi, D.*, "Mean field games for controlling coherent structures in nonlinear fluid systems", submitted arXiv preprint arXiv:2401.10356, 2024 [.pdf]
  • Cao, N., and Qi, D., "The maintenance of coherent vortex topology by Lagrangian chaos in drift-Rossby wave turbulence", Physics of Fluids, doi: 10.1063/5.0207687, 2024 [.pdf]
  • Qi, D.*, "Unambiguous models and machine learning strategies for anomalous extreme events in turbulent dynamical system", Entropy, doi: 10.3390/e26060522, 2024 [.pdf]
  • Chen, N., and Qi, D.*, "A physics-informed data-driven algorithm for ensemble forecast of complex turbulent systems", Applied Mathematics and Computation, doi: 10.1016/j.amc.2023.128480, 2023 [.pdf]
  • Qi, D.*, and Liu, J.-G., "High-order moment closure models with random batch method for efficient computation of multiscale turbulent systems", Chaos: An Interdisciplinary Journal of Nonlinear Science, doi: 10.1063/5.0160057, 2023 [.pdf]
  • Covington, J., Qi, D., and Chen, N., "Effective statistical control strategies in complex turbulent systems", Proc. R. Soc. A, doi: 10.1098/rspa.2023.0546, 2023 [.pdf]
  • Cao, N., and Qi, D., "Nearly-integrable flows and chaotic tangles in the dimits shift regime of plasmaedgeturbulence", Physics of Plasmas, Special Collection on Turbulence in Plasmas and Fluids, doi: 10.1063/5.0158013, 2023 [.pdf]
  • Qi, D.*, and Harlim, J., "A data-driven statistical-stochastic surrogate modeling strategy for complex nonlinear non-stationary dynamics", Journal of Computational Physics, doi: 10.1016/j.jcp.2023.112085 2023 [.pdf]
  • Qi, D.*, and Liu, J.-G., "A random batch method for efficient ensemble forecasts of multiscale turbulent systems", Chaos: An Interdisciplinary Journal of Nonlinear Science, doi: 10.1063/5.0129127, 2023 [.pdf]
  • Qi, D.*, and Harlim, J., "Machine learning-based statistical closure models for turbulent dy- namical systems", Philosophical Transactions A., doi: 10.1098/rsta.2021.0205, 2022 [.pdf]
  • Qi, D.*, and Vanden-Eijnden, E., "Anomalous statistics and large deviations of turbulent water waves past a step", AIP Advancesdoi: 10.1063/5.0082718, 2022 [.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", Physics of Plasmas, doi: 10.1063/5.0018943, 2021 [.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, doi: 10.1007/s40687-020-00219-2, 2021 [.pdf]
  • 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, doi: 10.1007/s40687-020-00219-2, 2020 [.pdf]
  • Qi, D.*, and Majda, A. J., "Flux-balanced two-field plasma edge turbulence in a channel geometry.", Physics of Plasmas, doi: 10.1063/1.5136281, 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, doi: 10.1073/pnas.191728511, 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., , 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.