Department of Mathematics

Purdue University

150 N University St

West Lafayette, IN 47907

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 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. The open research assistant and postdoc research associate positions include funding (to partially release teaching duties) for a student/postdoc who would like to study mathematical problems at the interface of statistical physics, geophysical fluid dynamics and plasma physics. Feel free to send me an e-mail and we can set up an appointment to chat about your interests.

- 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

- Fall 2024
*MA 504 Real Analysis*. - Spring 2024
*MA 303 Differential Equations and PDE*. - Fall 2023
*MA 573 Numerical Solutions of Ordinary Differential Equations*. - Spring 2023
*MA 510 Vector Calculus*. - Fall 2022
*MA 35301 Linear Algebra II*.

- Qi, D.*, and Liu, J.-G.,
*"High-Order Moment Closure Models with Random Batch Method for Efficient Computation of Multiscale Turbulent System"*, Chaos: An Interdisciplinary Journal of Nonlinear Science, submitted , 2023 [.pdf] - Covington, J., Qi, D., and Chen, N.,
*"Effective statistical control strategies in complex turbulent systems"*, Proc. R. Soc. A, submitted, 2023 [.pdf] - Cao, N., and Qi, D.,
*"Nearly-Integrable Flows and Chaotic Tangles in the Dimits Shift Regime of Plasma Edge Turbulence"*, Physics of Plasmas, Special Collection on Turbulence in Plasmas and Fluids, accepted, 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] - Chen, N., and Qi, D.*,
*" A Physics-Informed Data-Driven Algorithm for Ensemble Forecast of Complex Turbulent Systems."*, submitted, 2023 [.pdf] - Qi, D.*, and Harlim, J.,
*"Machine Learning-Based Statistical Closure Models for Turbulent Dynamical 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.*,
*"Unambiguous Models and Machine Learning Strategies for Anomalous Extreme Events in Turbulent Dynamical Systems."*, submitted, 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 (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)

- November 2022
*“Reduced-order models and data-driven closure strategies for turbulent systems"*, Applied Math & Analysis Seminar, Duke University. - November 2022
*“Statistical reduced-order models and data-driven closure strategies for turbulent systems"*, Machine Learning for Climate and Weather Applications, IMSI Workshop, Chicago, IL. - July 2022
*“Statistical reduced-order models and closure strategies for turbulent systems"*, SIAM Conference on Mathematics of Planet Earth (MPE22), Pittsburgh, PA. - May 2022
*“Reduced-order models and machine learning-based closure for turbulent systems"*, SIAM Conference on Uncertainty Quantification (UQ22), Atlanta, GA. - March 2022
*“Predicting extreme events and anomalous statistics of turbulent water waves"*, AMS Spring Central Meeting, West Lafayette, IN. - December 2021
*“Statistical reduced-order models and closure strategies for turbulent geophysical flows"*, AGU Fall Meeting, New Orleans, LA. - November 2021
*“Statistical reduced-order models and machine learning for turbulent geophysical flows"*, Storm Snacks, EAPS, Purdue University. - October 2021
*“Statistical reduced-order models and closure strategies for turbulent dynamical systems"*, Mathematics Colloquium, United States Naval Academy. - September 2021
*“Statistical reduced models and rigorous analysis for uncertainty quantification in turbulent dynamical systems"*, CCAM Seminar, Purdue University. - July 2021
*“Suppression of turbulent transport by zonal flows in magnetized plasmas (virtual)"*, SIAM Annual Meeting (AN21). - April 2021
*“Creation of coherent zonal structures from selective decay and secondary instability (virtual)"*, Analysis Group Seminar, University of Bremen. - March 2021
*“Predicting extreme events and anomalous features using a statistical dynamical model and machine learning (virtual)"*, Institute of Natural Sciences, Shanghai Jiao Tong University. - October 2019
*“Transition from drift wave turbulence to coherent zonal structures in plasma edge turbulence"*, 61st Annual Meeting of the APS Division of Plasma Physics (DPP), Fort Lauderdale, Florida. - July 2019
*“Statistical reduced models and rigorous analysis for uncertainty quantification of turbulent geophysical flows"*, Scientific Grand Challenges and New Perspectives in Applied Mathematics: Ocean, Atmosphere and Climate Sciences, University of Victoria, Canada. - July 2019
*“Reduced-order statistical models for predicting statistical responses and extreme events in geophysics"*, International Congress on Industrial and Applied Mathematics, Valencia, Spain. - December 2018
*“Statistical bounds for turbulent geophysical flows in uncertainty quantification"*, Applied Mathematics and Statistics Youth Forum, Peking University, Beijing, China. - December 2018
*“Rigorous statistical bounds in uncertainty quantification for turbulent geophysical flows"*, Graduate Student / Postdoc Seminar, Courant Institute, NY. - April 2018
*“Predicting Statistical Responses and Extreme Events in Turbulent Systems through Low-Dimensional Reduced-Order Models"*, SIAM Conference on Uncertainty Quantification, Garden Grove, CA. - December 2017
*“Low-Dimensional Reduced-Order Models for Statistical Response and Uncertainty Quantification in Turbulent Systems"*, AGU Fall Meeting, New Orleans, LA. - May 2017
*“Predicting Extreme Events for Passive Scalar Turbulence through Reduced-Order Models”*, SIAM Conference on Applications of Dynamical Systems (DS17), Snowbird, Utah. - December 2016
*“Statistical Response in Two-layer Baroclinic Turbulence for Uncertainty Quantification”*(poster), AGU Fall Meeting, San Francisco, CA. - October 2016
*“Low-Dimensional Reduced-Order Models for Statistical Response and Uncertainty Quantification”*, MURI 2016 workshop, New York University. - May 2016
*“Preventing Catastrophic Filter Divergence Using Adaptive Additive Inflation for Baroclinic Turbulence”*(poster), The 7th EnKF Data Assimilation Workshop, State College, PA. - April 2016
*“Improving Prediction Skill of Imperfect Turbulent Models through Empirical Information Theory”*, SIAM Conference on Uncertainty Quantification, EPFL, Lausanne, Switzerland. - January 2016
*“Improving Prediction Skill of Imperfect Turbulent Models through Empirical Information Theory”*, MURI 2016 Workshop, Courant Institute, NY. - January 2016 Uncertainty Quantification for Multiscale Stochastic Systems and Applications, UCLA, CA.
- August 2015
*“Blended Particle Filters for Large Dimensional Chaotic Dynamical Systems”*and*“Improving Prediction Skill of Imperfect Turbulent Models through Statistical Response and Information Theory”*, Mathematics of Geophysical Flows and Turbulence, Fudan University, Shanghai, China. - August 2015
*“Improving Prediction Skill of Imperfect Turbulent Models through Statistical Response and Information Theory”*, The 8th International Congress on Industrial and Applied Mathematics, Beijing, China. - August 2015 Frontiers of Applied and Computational Mathematics -- Celebrating Professor Björn Engquist's 70th Birthday, Peking University, Beijing, China.
- 29 June - 4 July 2014 Short Course on Stochastic Dynamics: Filtering and Rare Events, University of Warwick, UK.
- 30 June - 2 July 2014 Filtering High Dimensional Complex Systems, University of Warwick, UK.
- June 2014
*“Filtering Turbulent Signals in Fourier Space: Fourier Domain Kalman Filter”*, Short Course in High Dimensional Filtering, University of Warwick, UK. - 31 March - 3 April, 2014
*“Blended Particle Filters for Large Dimensional Chaotic Dynamical Systems”*, SIAM Conference on Uncertainty Quantification, Savannah, GA. - January 2014
*“Blended Particle Filter for Large Dimensional Chaotic Dynamical Systems”*, MURI 2014 Workshop, Courant Institute, NY. - June 2013 2013 Interdisciplinary Summer School: Data Assimilation in Geosciences, University of Maryland College Park, MD.

- 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.