Nicholas H. Nelsen

Ph.D. Candidate

Amazon AI4Science Fellow and NSF Graduate Research Fellow

California Institute of Technology

About Me

I am on the academic job market and seek full-time positions with start dates in Fall 2024

Welcome! I am a final year graduate student in the Division of Engineering and Applied Science at Caltech, where I work with my advisor Prof. Andrew M. Stuart. My research interests are in theory and algorithms for high-dimensional scientific and data-driven computation. Within applied and computational mathematics, some particular areas that I work in include scientific machine learning, inverse problems, uncertainty quantification, and statistical inference.

My current research centers on operator learning—regressing, from (noisy) data, operators that map between infinite-dimensional (function) spaces—with application to forward and inverse problems, especially those arising from parametric partial differential equations (PDEs) that model complex physical systems. To this end, I develop and utilize tools from machine learning, model reduction, numerical analysis, and statistics. Please refer to my curriculum vitae and my publications page to learn more about my background and research experience.

I am fortunate to be supported by the Amazon/Caltech AI4Science Fellows Program and by a NSF Graduate Research Fellowship. In 2020, I obtained my M.Sc. from Caltech, and before starting doctoral study in the fall of 2018, I worked on Lagrangian particle methods for PDEs as a summer research intern in the Center for Computing Research at Sandia National Laboratories. I obtained my B.Sc. (Mathematics), B.S.M.E., and B.S.A.E. degrees from Oklahoma State University in 2018.

nnelsen [at] caltech [dot] edu

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