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
Recent News
2023/10 (new): I am delivering an invited talk in MS23: Advances in V&V, Uncertainty Quantification, and Data-Driven Modeling at the Advances in Computational Mechanics (ACM 2023) conference in Austin, TX.
2023/09 (new): Our work on Error Bounds for Learning with Vector-Valued Random Features was accepted as a NeurIPS 2023 Spotlight paper!
2023/09: I am giving an invited talk in MS05: Numerical Meet Statistical Methods in Inverse Problems at the 11th Applied Inverse Problems Conference (AIP23) to be held in Göttingen, Germany.
2023/08: I am co-organizing the minisymposium MS831: Randomization for Simplified Machine Learning - Random Features and Reservoir Computers at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) in Tokyo, Japan.