James Martin

My central interest is to develop scientific models, mathematical techniques, and numerical algorithms that capitalize on emerging petascale computers to address previously intractable problems of great scientific and societal interest. Specifically, I seek to develop mathematical techniques and computational algorithms to quantify uncertainties through the solution of large-scale inverse problems, and to apply these techniques to challenging large-scale problems in computational physics and geodynamics.

Uncertainty quantification (UQ) is a crucial ingredient for simulation-based decision making. Yet, for large-scale problems with high-dimensional parameter uncertainties, UQ is effectively intractable today. Substantial work is needed to devise methods capable of estimating parameter uncertainty from comparisons of observations with model predictions (the inverse problem), as well as in propagating those uncertainties through the model. My goal is to capitalize on new ideas from statistics, stochastic PDEs, optimization, numerical analysis, inverse theory, scalable algorithms, and parallel supercomputing to create methods that have the potential to break the curse of dimensionality.

PUBLICATIONS

James Martin, "Discrete Mechanics and Optimal Control." Senior thesis, Caltech, 2006. Thesis Advisor: Prof. Jerrold Marsden.

Jonathan Galownia, James Martin, and Mark E. Davis. Aluminophosphate-based, microporous materials for blood clotting. Microporous and Mesorporous Materials, 92 (2006) p61-63.