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About me
Mathematical Modeling Software Engineer, math PhD.
Experience analyzing oncology data in Python and SQL and forecasting fusion simulation data in Python and MATLAB. Background in numerical analysis and machine learning with extensive multidisciplinary mathematical expertise.
PhD thesis: A Geometric Approach to Low-Rank Matrix and Tensor Completion. Researched low-rank matrix and tensor completion, and the maximum volume skeleton decomposition. Results include a new gradient descent skeleton decomposition based method for matrix and tensor completion, a new class of uniquely completable low-rank tensors, an upper bound on the number of dominant submatrices in a matrix in terms of the independence number of Johnson graphs, a greedy version of the maximum volume algorithm for finding dominant submatrices, and applying the maximum volume skeleton decomposition to simulate and compress high energy plasma simulation data.
Given the SCGSR award from the department of energy. Researched applications of the dynamic mode decomposition, a machine learning dimensionality reduction technique, to forecasting and compressing high energy plasma simulation data in MATLAB. We improved the prohibitive computational complexity of the low-rank approximation step in the dynamic mode decomposition from the order of n cubed required by the SVD to order n, while only increasing relative error from 1e-4 to 1e-3.