Troy Butler

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

Troy Butler is a Professor of Mathematics and the Associate Dean of Research and Creative Activities in the College of Liberal Arts and Sciences at CU Denver. 

Dr. Butler received his B.S. in Electrical Engineering (2003) and his M.S. (2005) and Ph.D. (2009) in Mathematics from Colorado State University. From 2009-12, Dr. Butler was a Postdoctoral Research fellow studying uncertainty quantification for hurricane storm surge simulations in the Computational Hydraulics Group housed within the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin. From 2012-13, Dr. Butler was a Research Scientist in the Department of Statistics at Colorado State University. Since Fall 2013, Dr. Butler has been a professor (obtaining the rank of full Professor in 2023) of mathematics at CU Denver, which has included various leadership roles such as serving as the Director for the university's Center for Computational Mathematics as well as the Associate Chair for his department. From 2023-2025, Dr. Butler was on detail at the National Science Foundation where he served as a Program Director for various programs including Computational Mathematics, the Mathematical Foundations of Artificial Intelligence, and Research Experiences for Undergraduates. Dr. Butler's own research in uncertainty quantification has been funded through various grants from the National Science Foundation, Department of Defense, and Department of Energy. In the summer of 2025, Dr. Butler began serving as the Associate Dean of Research and Creative Activities in the College of Liberal Arts and Sciences at CU Denver.

Selected Publications

• Local Stochastic Sensitivity Analysis For Dynamical Systems, N. Panda, J.H. Chaudhry, N. Klein, J. Carzon, T. Butler, Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4195-4203, 2025
• Stability and Convergence of Solutions to Stochastic Inverse Problems Using Approximate Probability Densities, T. Butler, R. Spence, T. Wildey, T.Y. Yen, International Journal for Uncertainty Quantification, Vol. 15 (4), pp. 21-51, 2025
• Sequential Maximal Updated Density Parameter Estimation for Dynamical Systems with Parameter Drift, C. del-Castillo-Negrete, R. Spence, T. Butler, C. Dawson, International Journal for Numerical Methods in Engineering, Vol. 126 (3), pp. e7618, 2025
• A Machine-Learning Enabled Framework for Quantifying Uncertainties in Parameters of Computational Models, T. Roper, H. Hakula, T. Butler, Computers & Mathematics with Applications, Vol. 182, pp. 184-212, 2025
• Learning Quantities of Interest from Dynamical Systems for Observation-Consistent Inversion, S. Mattis, K.R. Steffen, T. Butler, C. Dawson, D. Estep, Computer Methods in Applied Mechanics and Engineering, Vol. 388, pp. 114230, 2022
• Adjoint-based Accelerated Adaptive Refinement in Frequency Domain 3-D Finite Element Method Scattering Problems, J. Harmon, C. Key, D. Estep, T. Butler, B. Notaros, IEEE Transactions on Antennas and Propagation, Vol. 69 (2), pp. 940–949, 2021
• Optimal experimental design for prediction based on push-forward probability measures, T. Butler, J.D. Jakeman, and T. Wildey, Journal of Computational Physics, Vol. 416, pp. 109518, 2020
• Uncertainty Modeling of Carbon-Fiber-Reinforced Polymer-Confined Concrete in Acid-Induced Damage, Y.J. Kim, Y. Ji, and T. Butler, ACI Structural Journal, Vol. 116 (6), pp. 97-108, 2019
• Data-driven uncertainty quantification for predictive flow and transport modeling using support vector machines, J. He, S.A. Mattis, T.D. Butler, and C.N. Dawson, Computational Geosciences, Vol. 23 (4), pp. 631-645, 2019
• Combining Push-forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems, T. Butler, J. Jakeman, and T. Wildey, SIAM Journal on Scientific Computing, Vol. 40, No. 2, pp. A984-A1011, 2018.

Troy Butler has taught 13 different courses ranging from the 1000- to 8000-levels of his Department's curriculum. These include:

MATH 1376: Programming for Data Science 
MATH 3195: Linear Algebra and Differential Equations 
MATH 5070: Applied Analysis 
MATH 6131: Real Analysis 
MATH 7384: Mathematical Probability 
MATH 8660: Mathematical Foundations of Finite Element Methods