New York University

251 Mercer Street

New York, NY 10012-1185

Currently a post-doctoral research fellow at the Courant Institute of Mathematical Sciences and Center of Atmosphere and Ocean Science, New York 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 mentor is Prof. Andrew J Majda.

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.

You can find my CV here.

- 2017 Ph.D. in Mathematics/Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University.
- 2012 B.S. in Mathematics (major) and Physics (minor), Shanghai Jiao Tong University, China.

- Qi, D.* and Majda, A.J.,
*"Zonal jet creation from secondary instability of drift waves for plasma edge turbulence"*, submitted, 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"*, submitted, 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"*, submitted, 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)

- Fall 2019 Instructor of Prof. Majda's lectures on
*Uncertainty Quantification in Turbulent Dynamical Systems*. - Fall 2018 Instructor of Prof. Majda's lectures on
*Filtering Turbulent Signals in Complex Systems*. - Fall 2016 Co-instructor of Prof. Majda's lectures on
*Turbulent Dynamical Systems and Statistical Theories*. - Fall 2015 Co-instructor of Prof. Majda's lectures on
*Quantifying Uncertainty in Complex Turbulent Systems*.

- 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.