Publications
In addition to my published work below, my Google Scholar profile may be found here and my ORCID iD here.
Preprints
1. An operator learning perspective on parameter-to-observable maps
Daniel Zhengyu Huang, Nicholas H. Nelsen, and Margaret Trautner
Submitted February 2024.
[arXiv:2402.06031 cs.LG] [Code] [Data]
Journal Articles
2. Convergence rates for learning linear operators from noisy data
Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, and Andrew M. Stuart
SIAM/ASA Journal on Uncertainty Quantification, Vol. 11, No. 2, pp. 480–513, 2023.
[Download .pdf] [Official Version] [arXiv:2108.12515 math.ST] [Video]
1. The random feature model for input-output maps between Banach spaces
Nicholas H. Nelsen and Andrew M. Stuart
SIAM Journal on Scientific Computing, Vol. 43, No. 5, pp. A3212–A3243, 2021.
[Download .pdf] [Official Version] [arXiv:2005.10224 math.NA] [Code] [Data] [Short Video] [Long Video] [Poster]
Peer Reviewed Conference Papers
1. Error bounds for learning with vector-valued random features
Samuel Lanthaler and Nicholas H. Nelsen
Advances in Neural Information Processing Systems, Vol. 36, pp. 71834--71861, 2023 (NeurIPS 2023 spotlight paper).
[Download .pdf] [Official Version] [arXiv:2305.17170 stat.ML] [Code] [Video] [Poster]
Lecture Notes
1. Operator-valued kernels
Nicholas H. Nelsen
Chap. III.3, pp. 286–297, in ACM 204: Matrix Analysis by Joel A. Tropp, Caltech CMS Lectures Notes Winter 2022.
Theses
2. On partial differential equations modified with fractional operators and integral transformations
Nicholas H. Nelsen
Bachelor's Honors Thesis, Oklahoma State University, Department of Mathematics, 2018.
[Download .pdf] [Official Version]
1. A reduced order framework for optimal control of nonlinear partial differential equations
Nicholas H. Nelsen
Bachelor's Honors Thesis, Oklahoma State University, School of Mechanical and Aerospace Engineering, 2018.
Miscellaneous
3. Diastolic vortex alterations with reducing left ventricular volume: an in vitro study
Milad Samaee, Nicholas H. Nelsen, Manikantam G. Gaddam, and Arvind Santhanakrishnan
Journal of Biomechanical Engineering, Vol. 142, No. 12, 2020.
[Download .pdf] [Official Version]
2. Lagrangian particle methods for the shallow water equations in varied geometries
Nicholas H. Nelsen and Peter A. Bosler
Sandia National Laboratories Center for Computing Research Summer Proceedings 2018, pg. 163-182, SAND2019-5093R, 2019.
[Download .pdf] [Official Version]
1. Advanced and exploratory shock sensing mechanisms
Nicholas H. Nelsen et al.
Sandia National Laboratories Technical Report SAND2017-10221, 2017.