Greetings and Current News

Welcome to the personal website of Troy Butler. Below is some current news related to my professional activities.

The board of regents recently awarded me tenure, promotion to the rank of Associate Professor, and approved my sabbatical with full pay. Tenure is effective as of April 2019, rank of Associate Professor is effective in Fall 2019, and I am taking my sabbatical in Spring 2020.

Recent Funded–Research Highlights

  • Collaborative Research: Construction and Analysis of Numerical Methods for Stochastic Inverse Problems with Application to Coastal Hydrodynamics (NSF DMS-1818941) (lead PI, multi-institional grant, CU Denver portion $175,000).

    • Moving towards v3.0 release of BET to include sampling algorithms based on push-forward measures

    • First all–hands meeting is scheduled at CU Denver, June 10–11, 2019.

Recent Publication Highlights

  • Accepted papers that are in press:

    • Enhancing piecewise defined surrogate response surfaces with adjoints on sets of unstructured samples to solve stochastic inverse problems will appear soon in the International Journal for Numerical Methods in Engineering

    • Uncertainty Modeling of CFRP-confined Concrete in Acid-induced Damage will appear soon in ACI Structural Journal

  • Papers in review:

    • A Posteriori Error Estimation and Adaptive Discretization Refinement Using Adjoint Methods in CEM: A Study with a One-Dimensional Higher-Order FEM Scattering Example is revised/resubmitted and in review.

  • Nearing submission (working titles):

    • Optimal Experimental Design for Prediction Based on Push-Forward Probability Measures

    • A New Approach to Optimal Experimental Design Using Singular Values of Jacobians for Nonlinear Observable Maps

    • Data–Consistent Inversion for Stochastic Parameter–to–Observable Maps

    • A Data–Consistent Approach for Parameter Estimation

Teaching News

  • I am teaching the special topics Math 5027 in Fall 2019. This course is intended as a type of “bridge analysis” to help improve graduate student success.

Skills

Python

Proficient

Mathematics

Advanced

Machine Learning / AI

Beginner

Experience

 
 
 
 
 

Associate Professor

Mathematical and Statistical Sciences
University of Colorado Denver

Aug 2019 – Present
 
 
 
 
 

Director

Center for Computational Mathematics
University of Colorado Denver

Aug 2014 – Jul 2017
 
 
 
 
 

Assistant Professor

Mathematical and Statistical Sciences
University of Colorado Denver

Aug 2013 – Jul 2018
 
 
 
 
 

Research Scientist Lv. II

Statistics
Colorado State University

Aug 2012 – Jul 2013
 
 
 
 
 

Research Associate

Institute for Computational Engineering and Sciences
The University of Texas at Austin

Sep 2011 – Jul 2012
 
 
 
 
 

Postdoctoral Research Fellow

Institute for Computational Engineering and Sciences
The University of Texas at Austin

Aug 2009 – Aug 2012

Research
Funding
(Recent)

Collaborative Research: Construction and Analysis of Numerical Methods for Stochastic Inverse Problems with Application to Coastal Hydrodynamics (NSF DMS-1818941).

National Science Foundation
Division of Mathematical Sciences Aug 2018 – Jul 2021
Lead PI of multi–institutional grant with co-PI’s at Colorado State University and The University of Texas at Austin. Total Funding: USD(355k) (CU–Denver portion: USD(175k))

Development of Uncertainty Quantification and Design Approaches and Solutions for CREATE/SENTRi.

Department of Defense
High Performance Computing Modernization Program (subcontract through Colorado State University) Mar 2018 – Jul 2022
Aiding in UQ and V&V analyses for computational electromagnetics applications. USD(102.3k)

Projects

*

A python library for solving UQ problems with measure theory.

Recent & Upcoming Talks

Mar 26, 2019 3:00 PM Numerical Analysis Seminar, Department of Mathematics, North Carolina State University

Feb 27, 2019 2:15 PM Minisymposium on Exploiting Model Hierarchies, Sparsity and Low-rank Structure of Large-scale Bayesian Computation, SIAM CSE 19, Spokane, WA

Featured Publications

In SISC

We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on parameters is propagated through the approximate model to produce a probability density, often called a push-forward probability density, on a set of quantities of interest (QoI). The inverse problem considered in this paper seeks to update an initial probability density assumed on model input parameters such that the subsequent push-forward of this updated density through the parameter-to-QoI map matches a given probability density on the QoI. We prove that the densities obtained from solving the forward and inverse problems, using approximate models, converge to the true densities as the approximate models converge to the true models. Numerical results are presented to demonstrate convergence rates of densities for sparse grid approximations of parameter-to-QoI maps and standard spatial and temporal discretizations of PDEs and ODEs.
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In SISC

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data on quantities of interest. The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a posterior probability measure that when propagated through the deterministic model produces a push-forward measure that exactly matches the observed probability measure on the data. Our approach for finding such posterior measures, which we call consistent Bayesian inference or push-forward based inference, is simple and only requires the computation of the push-forward probability measure induced by the combination of a prior probability measure and the deterministic model. We establish existence and uniqueness of observation-consistent posteriors and present both stability and error analyses. We also discuss the relationships between consistent Bayesian inference, classical/statistical Bayesian inference, and a recently developed measure-theoretic approach for inference. Finally, analytical and numerical results are presented to highlight certain properties of the consistent Bayesian approach and the differences between this approach and the two aforementioned alternatives for inference.
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Recent Publications

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Many approaches for solving stochastic inverse problems suffer from both stochastic and deterministic sources of error. The finite …
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We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We …
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Specification of hydraulic conductivity as a model parameter in groundwater flow and transport equations is an essential step in …
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Popular Topics

a-posteriori-error-estimates a-posteriori-error-estimation academic adjoint data-consistent-inversion machine-learning model-selection optimal-experimental-design sensitivity-analysis storm-surge surrogate uncertainty-quantification

Contact

  • (303) 315 1734
  • Room 4008, Student Commons Building, University of Colorado Denver
  • [Fall Semester]
    Monday 1:00 p.m. to 2:00 p.m.
    Wednesday 2:00 p.m. to 3:00 p.m.