Mathematics Building 140A
Ill-posed Inverse Problems, Computational Algorithms, Geosciences, Geophysics
Opportunities for Students
Dr. Mead is looking for students interested in computational applied mathematics and statistics, with interest both in the theory and development of algorithms.
Ill-posed inverse problems arise in many applications where data are combined with mathematical models in order to build better predictive models. Currently, my application focus is geophysics, and in particular recovering an image of the subsurface from measurements at the surface.
Computing PhD -Emphasis in Data Science, anticipated graduation May 2021
Regularization is a common technique for solving ill-posed inverse problems. However, additional information contained in a regularization operator is typically not scientifically based, and does little more than mathematically allow a solution. We explore using additional data to regularize and in particular, we seek to identify which data reduce the search space of optimal parameters. A reduced search space can alleviate the problem of finding local minima, and hence reduce the computational cost of generating a convergent sequence of solutions in a nonlinear inversion.