Research interests/expertise
Uncertainty quantification, multifidelity Monte Carlo, inverse problems, predictive modeling, scientific computing, fluid dynamics in shallow water systems and aerospace systems
Current Research Projects
Multifidelity Monte Carlo
Measure Theorteic Interpretation of Sample Based Numerical Integration
Python-based framework for running batches of parallel ADCIRC simulations with varying parameters (Manning's n). Includes documentation for a Python interface to a slightly modified version of GridData (Griddata_v1.32.F90). GridData is a FORTRAN program originally developed by Seizo Tanaka (ST3) and C.H.Lab., University of Notre Dame. GitHub Repo
T. Butler, L. Graham, S. Mattis, and S. Walsh, A Measure-Theoretic Interpretation of Sample Based Numerical Integration with Applications to Inverse and Prediction Problems Under Uncertainty, SIAM Journal on Scientific Computing, February 2016, in REVIEW, pre-print.
TBD
Presentations
Measure-Theoretic Methods for Uncertainty Quantification, Applied Mathematics Colloquium, Columbia University, New York, NY, November 2016
Inverse Sensitivity Analysis for Storm Surge Models, XSEDE Scholars Program Webinar Series, Online, January 2013
NSBE Graduate Student Panel, University of Texas at Austin NSBE Chapter Meeting, Austin, TX, October 2012
Publications
L. Graham, C. Dawson, T. Butler, S. Walsh, A Measure-Theoretic Algorithm for Estimating Bottom Friction in a Coastal Inlet: Case Study of Bay St. Louis during Hurricane Gustav (2008), April 2016, in PRODUCTION, doi: 10.1175/MWR-D-16-0149.1 .
T. Butler, L. Graham, D. Estep, C. Dawson, J.J. Westerink, Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models, Advances in Water Resources, Available online 3 February 2015, ISSN 0309-1708, doi:10.1016/j.advwatres.2015.01.011.
T. Butler, D. Estep, S. Tavener, T. Wildey, C. Dawson, and L. Graham, Solving stochastic inverse
problems using sigma-algebras on contour maps," 2014, arXiv preprint arXiv:1407.3851
Hartzell, C.M.; Graham, L.C.; Tao, T.S.; Goldberg, H.R.; Carpena-Nunez, J.; Racek, D.M.; Taylor, C.E.; Norton, C.D., "Data system design for a hyperspectral imaging mission concept," Aerospace conference, 2009 IEEE , vol., no., pp.1-21, 7-14 March 2009, doi: 10.1109/AREO.2009.4839507