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University of Colorado Denver College of Liberal Arts and Sciences

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Faculty & Staff Directory

Troy Butler, Ph.D.

Assistant Professor

Office Location: CU Building 644
Phone: (303) 315-1734

Areas of Expertise:

 Applied Mathematics

Education & Degrees

Ph.D., Mathematics, Colorado State University, 2009
M.S., Mathematics, Colorado State University, 2005
B.S., Electrical Engineering, Colorado State University, 2003


Troy Butler recently joined the department as an Assistant Professor. Currently, Troy's research is supported by grants from the NSF and DOE.
From 2012-2013, Troy was a research scientist at Colorado State University (CSU) working in Dr. Don Estep's research group on uncertainty quantification. From 2009-2012, Troy began his postdoctoral work an ICES Postdoctoral Research Fellow and was promoted to a Research Associate in the Computational Hydraulics Group directed by Dr. Clint Dawson within the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin.

Troy's current projects include developing and applying novel uncertainty quantification techniques to a variety of real-world problems using real data involving storm surge from hurricanes and tropical cyclones in the Gulf of Mexico, subsurface contaminant spread with a model problem based on a chromium plume beneath Los Alamos National Laboratory, and detecting damage in vibrating beams by passive observation networks.

Select Publications

Propagation of uncertainties using improved surrogate models, T. Butler, C. Dawson, and T. Wildey, SIAM/ASA J. Uncertainty Quantification 1-1 (2013), pp. 164-191

Improving Short-Range Ensemble Kalman Storm Surge Forecasting Using Robust Adaptive Inflation., Altaf, M. U., T. Butler, X. Luo, C. Dawson, T. Mayo, I. Hoteit, Monthly Weather Review, Vol. 141, No. 8, (2013), pp. 2705–2720

A numerical method for solving a stochastic inverse problem for parameters, T. Butler and D. Estep, Annals of Nuclear Energy, 52 (2013), pp. 86–94

Data Assimilation within the Advanced Circulation (ADCIRC) Modeling Frameowork for Hurricane Storm Surge Forecasting, T. Butler, M.U. Altaf, C. Dawson, I. Hoteit, X. Luo, and T. Mayo, Monthly Weather Review, Vol. 140, No. 7. (2012), pp. 2215-2231

Reparameterization for statistical state estimation applied to differential equations, T. Butler, M. Juntunen, Journal of Computational Physics 231 (2012), pp. 2641-2654

A posteriori error analysis of parameterized linear systems using spectral methods, T. Butler, P. Constantine, T. Wildey, SIAM Journal on Matrix Analysis and Applications 33 (2012), pp. 195-209

A computational measure-theoretic approach to inverse sensitivity problems II: A posteriori error analysis, T. Butler, D. Estep, J. Sandelin, SIAM Journal on Numerical Analysis 50 (2012), pp. 22-45

A measure-theoretic computational method for inverse sensitivity problems I: Method and Analysis, J. Breidt, T. Butler, D. Estep, SIAM Journal on Numerical Analysis 49 (2011), pp. 1836-1859

A posteriori error analysis of stochastic differential equations using polynomial chaos expansions, T. Butler, C. Dawson, T. Wildey, SIAM Journal on Scientific Computing 33 (2011), pp. 1267-1291

Courses Taught

Courses taught at Colorado State University:

Spring 2013: Statistics for Engineers and Scientists
Fall 2012: Statistics for Engineers and Scientists
Spring 2008: Introduction to Ordinary Differential Equations
Fall 2008: Short Course on Sensitivity Analysis
Summer 2005: Calculus for Physical Scientists III
Spring 2005: Calculus for Physical Scientists II
Fall 2004: Calculus for Physical Scientists I
Summer 2004: Math in the Social Sciences
Spring 2004: Calculus for Physical Scientists I
Fall 2003: Calculus for Physical Scientists I

Courses taught at The University of Texas at Austin:

Fall 2011: Engineering Computation