Eric Kostelich

President's Professor
Faculty
TEMPE Campus
Mailcode
1804

Biography

Eric Kostelich is interested in nonlinear dynamics, uncertainty quantification, and mathematical biology. He is one of the principal developers of a computationally efficient and very accurate method for estimating the initial conditions of numerical weather models from sparse sets of noisy observations, a procedure called data assimilation. Kostelich has been working on related problems in data assimilation for “space weather” in the ionosphere. He is also interested in questions of uncertainty quantification and parameter identification in mathematical models, including those related to the growth and treatment of cancer, such as prostate cancer and malignant glioma. He has co-authored (with Professor Dieter Armbruster) an undergraduate textbook on differential equations.

Fax

480/965-8119

Education

Ph.D. University of Maryland-College Park 1985

Google Scholar

Research Interests

Data assimilation, uncertainty quantification, mathematical biology, and high-performance computing.

Research Group

Professor Kostelich directs a research program, funded by the Arizona Biomedical Research Commission, on data assimilation and mathematical modeling of glioblastoma, a virulent form of brain cancer.  This work is a collaboration with co-principal investigator Yang Kuang at ASU and Dr. Mark Preul and Dr. Charles Quarles at the Barrow Neurological Institute.

Dr. Kostelich also has research interests in atmospheric modeling and data assimilation, which he pursues in collaboration with Professors Alex Mahalov and Mohamed Moustaoui at ASU.

With Professor Wenbo Tang, Professor Kostelich directs the (AM)^2 Applied Mathematics Reseach Experience for Undergraduates Program at ASU in partnership with Maricopa Community Colleges, which is funded by the National Science Foundation. This program provides intensive summer research experiencesfor selected mathematics majors and for community college students with interests in the mathematical sciences and related fields.

Publications

  • L. Han, S. Eikenberry, C. He, L. Johnson, M. C. Preul, E. J. Kostelich, and Y. Kuang, “Patient-specific parameter estimates of glioblastoma multiforme growth dynamics from a model with explicit birth and death rates,” Mathe- matical Biosciences and Engineering, 16 (2019), 5307–5323. 
  • T.L.Stepien,E.J.Kostelich,andY.Kuang,“Mathematics+Cancer:Anundergraduatecourseimplementingap- plications of differential equations,” SIAM Review, in press.
  • Z. Wu, T. Phan, J. Baez, Y. Kuang, and E. J. Kostelich, “Predictability and identifiability assessment of models for prostate cancer under androgen suppression therapy,” Mathematical Biosciences and Engineering, 16 (2019), 3512– 3536. 
  • J. Durazo, E. J. Kostelich, and A. Mahalov, “ Local Ensemble Transform Kalman Filter for ionospheric data as- similation: Observation influence analysis during a geomagnetic storm event,” Journal of Geophysical Research— Space Physics 122 (2017), 9652–9669.
  • E. M. Rutter, T. L. Stepien, B. J. Anderies, J. D. Plasencia, E. C. Woolf, A. C. Scheck, G. H. Turner, Q. Liu, D. Frakes, V. Kodibagkar, Y. Kuang, M. C. Preul, and E. J. Kostelich, “Mathematical analysis of glioma growth in a murine model,” Scientific Reports 7 (2017), 2508.
  • J. Durazo, E. J. Kostelich, A. Mahalov, and W. Tang, “Observing system experiments with an ionospheric elec- trodynamics model,” Physica Scripta 91 (2016), 044001.
  • N. L. Martirosyan, E. M. Rutter, W. L. Ramey, E. J. Kostelich, Y. Kuang, and M. C. Preul, “Mathematically modeling the biological properties of gliomas: A review,” Mathematical Biosciences and Engineering 12 (2015), 879–905.
  • M. Moustaoui, A. Mahalov, and E. J. Kostelich. A numerical method based on leapfrog and a fourth-order implicit time filter. Monthly Weather Review (2014).
  • T. Bellsky, E. J. Kostelich, and A. Mahalov. Kalman filter data assimilation: Targeting observations and parameter estimation. Chaos (2014).
  • M. Moustaoui, A. Mahalov, and E. J. Kostelich. A numerical method based on leapfrog and a fourth-order implicit time filter. Monthly Weather Review (2013).
  • J. McDaniel, E. J. Kostelich, Y. Kuang, J. Nagy, M. C. Preul, N. Z. Moore and N. L. Matirosyan. Data Assimi- lation in Brain Tumor Models. Mathematical Methods and Models in Biomedicine (2013).
  • E. J. Kostelich, Y. Kuang, J. McDaniel, N. Z. Moore, N. L. Martirosyan, and M. C. Preul. Accurate state estimation from uncertain data and models: An application of data assimilation to mathematical models of human brain tumors. Biology Direct (2011).
  • H. Li, J. Liu, E. Fertig, E. Kalnay, E. Kostelich, and I. Szunyogh. Improved analyses and forecasts with AIRS temperature retrievals using the Local Ensemble Transform Kalman Filter. Journal of Tropical Meteorology (2011).
  • J. A. Aravequia, I. Szunyogh, E. J. Fertig, E. Kalnay, D. Kuhl, and E. J. Kostelich. Evaluation of a strategy for the assimilation of satellite radiance observations with the local ensemble Kalman filter. Monthly Weather Review (2011).
  • M.J. Hoffman, S.J. Greybush, R.J. Wilson, G. Gyarmati, R.N. Hoffman, E. Kalnay, K. Ide, E.J. Kostelich, T. Miyoshi, and I. Szunyogh,. An ensemble Kalman filter data assimilation system for the Martian atmosphere: Implementation and simulation experiments. Icarus (2010).
  • J. Liu, H. Li, E. Kalnay, E.J. Kostelich, and I. Szunyogh. Univariate and multivariate assimilation of AIRS humidity retrievals with the Local Ensemble Transform Kalman Filter. Monthly Weather Review (2009).
  • S. Eikenberry, T. Sankar, M.C. Preul, E.J. Kostelich, C. Thalhauser, and Y. Kuang. Virtual glioblastoma: Growth, migration, and treatment in a three-dimensional mathematical model. Cell Proliferation (2009).
  • I Szunyogh, Eric Kostelich, G Gyarmati, E Kalnay, B Hunt, E Ott, E Satterfield, J Yorke. A local ensemble Kalman filter data assimilation system for the NCEP global model. Tellus (2008).
  • I. Szunyogh, E. J. Kostelich, G. Gyarmati, E. Kalnay, B. R. Hunt, E. Ott, E. Satter?eld, and J. A. Yorke. A local ensemble Kalman Filter data assimilation system for the NCEP global model. Tellus A (2008).
  • J. Liu, E. Fertig, H. Li, E. Kalnay, B. R. Hunt, E. J. Kostelich, I. Szunyogh, and R. Todling. Comparison between the Local Ensemble Transform Kalman Filter and PSAS in the NASA ?nite-volume GCM: Perfect model experiments. Nonlin. Proc. Geophys (2008).
  • R. N. Hoffman, R. M. Ponte, E. J. Kostelich, A. Blumberg, I. Szunyogh, S. V. Vinogradov, and J. M. Henderson. A simulation study using a local ensemble transform Kalman ?lter for data assimilation in New York Harbor. J. Atmos. Ocean Tech (2008).
  • B Hunt, Eric Kostelich, I Szunyogh. Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Phyisca D (2007).
  • D Kuhl, J Yorke, I Szunyogh, Eric Kostelich, D Patil, G Gyarmati, M Oczkowski, B Hunt, E Kalnay, E Ott. Assessing predictability with a local ensemble Kalman filter. J. Atmos. Sci (2007).
  • I Szunyogh, Eric Kostelich, G Gyarmati, D Patil, B Hunt, E Kalnay, E Ott, J Yorke. Assessing a local ensemble Kalman filter: Perfect model experiments with the NCEP global model. Tellus (2005).
  • B Hunt, E Kalnay, Eric Kostelich, E Ott, D Patil, T Sauer, I Szunyogh, J Yorke, A Zimin. Four-dimensional ensemble Kalman filtering. Tellus A (2004).
  • E Ott, B Hunt, I Szunyogh, A Zimin, Eric Kostelich, M Corazza, E Kalnay, D Patil, J Yorke. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A (2004).
  • E Ott, B Junt, I Szunyogh, A Zimin, Eric Kostelich, M Corazza, E Kalnay, D Patil, J Yorke. Estimating the state of large spatio-temporally chaotic systems. Phys. Lett. A (2004).
  • B Zeff, D Lanterman, R McAllister, R Roy, Eric Kostelich, D Lathrop. Measuring intense rotation and dissipation in turbulent flows. Nature (2003).
  • Eric Kostelich, D Armbruster, Y Lai. Reply to 'Comment on "Intermittency in Chaotic Rotations"'. Phys. Rev. E (2001).
  • Eric Kostelich. Bootstrap estimates of chaotic dynamics. Phys. Rev. E (2000).
  • Eric Kostelich, D Armbruster, Y Lai. Intermittency in chaotic rotations. Phys. Rev. E (2000).
  • Eric Kostelich, M Dhamala, Y Lai. Detecting unstable periodic orbits from transient chaotic time series. Phys. Rev. E (2000).
  • E. O’Neill-Carrillo, G. T. Heydt, E. J. Kostelich, S. S. Venkata, and A. Sundaram, “Nonlinear deterministic modeling of highly varying loads,” IEEE Transactions on Power Delivery 14 (1999), 537–542.
  • E. O’Neill-Carrillo, E. J. Kostelich and G. T. Heydt, “Chaotic phenomena in power systems: Detection and applications,” Electric Machines and Power Systems 27 (1999), 79–92.
  • E. Bollt and E. J. Kostelich, “Optimal targeting of chaos,” Phys. Lett. A 245 (1998), 399–406.
  • E. J. Kostelich, “The analysis of chaotic time series data,” Systems & Control Letters 31 (1997), 313–319.
  • E. J. Kostelich, I. Kan, C. Grebogi, E. Ott, and J. A. Yorke, “Unstable dimension variability: a source of nonhy- perbolicity in chaotic systems,” Physica D 109 (1997), 81–90.
  • S. Boccaletti, A. Farini, E. J. Kostelich and F. T. Arecchi, “Adaptive Targeting of Chaos,” Physical Review E 55 (1997), 4845–4848.
  • “Control of Chaos: Impact Oscillators and Targeting,” with E. Barreto, F. Casas, and C. Grebogi, in IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems, ed. by D. H. van Campen. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1997, pp. 17–26.
  • E. J. Kostelich, J. A. Yorke and Z. You, “Plotting stable manifolds: error estimates and noninvertible maps,” Physica D 93 (1996), 210–222.
  • A.Palacios,D.Armbruster,E.J.KostelichandE.Stone,“Analyzingthedynamicsofcellularflames,”PhysicaD 96 (1996), 132–161.
  • “Targeting and Control of Chaos,”with E.Barreto, in Control and Chaos, ed. by K.Judd, A.Mees, K.L.Teo and T. Vincent. Boston: Birkhäuser, 1997, pp. 158–169.
  • E. Barreto, E. J. Kostelich, C. Grebogi, E. Ott, and J. A. Yorke, “Efficient switching between controlled unstable periodic orbits in higher dimensional chaotic systems,” Physical Review E 51 (1995), 4169–4172.
  • C.S.Daw,C.E.A.Finney,M.Vasudevan,N.A.vanGoor,K.Nguyen,D.D.Bruns,E.J.Kostelich,C.Grebogi, E. Ott, and J. A. Yorke, “Self organization and chaos in a fluidized bed,” Physical Review Letters, 75 (1995), 2308–2311.
  • Y.-C. Lai, C. Grebogi, and E. J. Kostelich, “Extreme final state sensitivity in asymmetric spatiotemporal chaotic systems,” Physics Letters A 196 1994, 206–212.
  • R.Heiland,D.Armbruster,andE.J.Kostelich,“KLTOOL:atooltoanalyzespatio-temporalcomplexity,”Chaos 4 (1994), 421–424.
  • “Uncertain determinism,” Nature 465 (9 Sept. 1993), 106–107.
  • E. J. Kostelich and T. Schreiber, “Noise reduction in chaotic time series data: a survey of common methods,”
    Physical Review E, 48 (1993), 1752–1763.
  • E.J.Kostelich,C.Grebogi,E.OttandJ.A.Yorke,“Higherdimensionaltargeting,”PhysicalReviewE47(1993),
    305–310.
  • D. Armbruster, R. Heiland, E. J. Kostelich and B. Nicolaenko, “Phase space analysis of bursting behavior in Kolomogorov flow,” Physica D 58 (1992), 392–401.

  • E. J. Kostelich, “Problems in estimating dynamics from data,” Physica D 58 (1992), 138–152.

  • Z. You, E. J. Kostelich, and J. A. Yorke, “Calculating stable and unstable manifolds,” Bifurcation and Chaos 1 (1991), 605–624.

  • E. J. Kostelich and J. A. Yorke, “Noise Reduction: Finding the Simplest Dynamical System Consistent with the Data,” by Physica D 41 (1990), 183–196.

 

  • D.P. Lathrop and E.J. Kostelich, “The Characterization of an Experimental Strange Attractor by Periodic Orbits,” Physical Review A 40 (1989), 4028–4031.
  • W.L. Ditto, S. Rauseo, R. Cawley, C. Grebogi, G.-H. Hsu, E.J. Kostelich, E. Ott, H.T. Savage, R.Seyman, M.L. Spano, and J. A. Yorke, “Experimental Observation of Crisis-Induced Intermittency and Its Critical Exponent,” Physical Review Letters 63 (1989), 923–926.
  • E. J. Kostelich and H. L. Swinney, “Practical Considerations in Estimating Dimension from Time Series Data,” Physica Scripta 40 (1989), 436–441.
  •  E. J. Kostelich and J. A. Yorke, “Noise Reduction in Dynamical Systems,” Phys. Rev. A 38 (Aug. 1988), 1649– 1652.
  • W. F. Langford, R. Tagg, E. J. Kostelich, H. L. Swinney, and M. Golubitsky, “Primary Instabilities and Bicriti- cality in Flow between Counterrotating Cylinders,” Physics of Fluids, 31 (1988), 776–785.

 

  • C. Grebogi, E. J. Kostelich, E. Ott, and J. A. Yorke, “Multi-Dimensioned Intertwined Basin Boundaries and the Kicked Double Rotor,” Physica D 25 (1987), 347–360.
  • E. J. Kostelich and J. A. Yorke, “Lorenz Cross Sections of the Chaotic Attractor of the Kicked Double Rotor,” Physica D 24 (1987), 263–278.

 

 

 

 

 

 

 

 

Research Activity

Courses

Summer 2019
Course Number Course Title
APM 792 Research
Spring 2019
Course Number Course Title
MAT 272 Calc w/Analytic Geometry III
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
APM 792 Research
MAT 799 Dissertation
APM 799 Dissertation
Fall 2018
Course Number Course Title
MAT 394 Special Topics
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 499 Individualized Instruction
APM 525 High-Performance Computing
MAE 598 Special Topics
APM 792 Research
MAT 799 Dissertation
Summer 2018
Course Number Course Title
MAT 495 Undergraduate Research
APM 792 Research
Spring 2018
Course Number Course Title
MAT 272 Calc w/Analytic Geometry III
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
APM 792 Research
MAT 799 Dissertation
APM 799 Dissertation
Fall 2017
Course Number Course Title
MAT 275 Modern Differential Equations
MAT 394 Special Topics
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 494 Special Topics
APM 792 Research
MAT 799 Dissertation
Summer 2017
Course Number Course Title
MAT 494 Special Topics
APM 792 Research
Spring 2017
Course Number Course Title
MAT 272 Calc w/Analytic Geometry III
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 494 Special Topics
APM 792 Research
MAT 799 Dissertation
APM 799 Dissertation
Fall 2016
Course Number Course Title
MAT 272 Calc w/Analytic Geometry III
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 494 Special Topics
APM 525 High-Performance Computing
MAE 598 Special Topics
APM 792 Research
MAT 799 Dissertation
Summer 2016
Course Number Course Title
MAT 494 Special Topics
APM 792 Research
Spring 2016
Course Number Course Title
MAT 272 Calc w/Analytic Geometry III
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 494 Special Topics
APM 792 Research
MAT 799 Dissertation
APM 799 Dissertation
Fall 2015
Course Number Course Title
MAT 272 Calc w/Analytic Geometry III
MAT 394 Special Topics
MAT 492 Honors Directed Study
MAT 494 Special Topics
APM 792 Research
MAT 799 Dissertation
Summer 2015
Course Number Course Title
MAT 494 Special Topics
APM 792 Research
Spring 2015
Course Number Course Title
MAT 275 Modern Differential Equations
MAT 493 Honors Thesis
MAT 494 Special Topics
MAT 499 Individualized Instruction
APM 790 Reading and Conference
APM 792 Research
MAT 799 Dissertation

Honors/Awards

  • ASU President's Professor (2012 - present)
  • Special recognition, ASU Parents Association Professor of the Year, 2009
  • Charles Wexler Teaching award, 2018
  • National Science Foundation Graduate Fellowship
  • Morehead Scholar, University of North Carolina at Chapel Hill

Professional Associations

Member of the American Mathematical Society, Society for Industrial and Applied Mathematics, American Physical Society, and American Association for the Advancement of Science.

Service

  • SIAM Journal of Applied Dynamical Systems, Associate editor and member of the editorial board (2013 - present)
  • Goldwater Scholarship selection committee, member (2007 - present)
  • University and CLAS Senate, SoMSS Senator (2013 - present)
  • Program chair, SIAM Activity Group on Applied Math Education (2016 - 2018)
  • Participant on various National Science Foundation review panels (2006 - present)

Graduate Faculties / Mentoring History

Professor Kostelich is one of the directors of the Hands-On School for Complex Systems Research, a program administered by the International Center for Theoretical Physics in Trieste, Italy.  The School is an intensive, two-week program for early-career scientists from developing countries.  Participants work on tabletop laboratory experiments, mathematical modeling, and oral and written scientific communication in English of their own research.