Nicholas H. Nelsen
NSF Graduate Research Fellow and Ph.D. Candidate
California Institute of Technology
About Me
Welcome! I am a fourth 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.
My current work is centered 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 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 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
2022/08: I am giving an invited virtual talk about my joint work on operator learning in MS1714: Advances in Scientific Machine Learning for High-Dimensional Many-Query Problems, part of the WCCM--APCOM in Yokohama, Japan.
2022/06: I am giving an invited talk about our work on learned surrogates for parametric PDEs in MS210: Reduced-Order and Surrogate Models for Mechanics of Porous Media, part of the Engineering Mechanics Institute Conference at Johns Hopkins University, Baltimore, MD.
2022/05: I am giving an invited virtual talk about "Noisy Linear Operator Learning as an Inverse Problem" in WS3: PDE-constrained Bayesian inverse problems, part of the Computational Uncertainty Quantification thematic programme at the Erwin Schrödinger Institute in Vienna, Austria.
2022/05: I am giving an invited virtual talk about "Bayesian Posterior Contraction for Linear Operator Learning" at the AMS Spring Western Sectional Meeting Special Session on Mathematical Advances in Bayesian Statistical Inversion and Markov Chain Monte Carlo Sampling Algorithms.
2022/04: I am co-organizing a minisymposium on Operator Learning in PDEs, Inverse Problems, and UQ at SIAM UQ22 in Atlanta, GA, where I will also be speaking about our recent work on "Convergence Rates for Learning Linear Operators from Noisy Data".
2022/01: This year I am co-organizing the Caltech Department of Computing and Mathematical Sciences CMX Student/Postdoc Seminar.