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] [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, 2024 (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.

[Download .pdf] [Official Version]

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. 

[Download .pdf] [Official Version

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. 

[Download .pdf] [Official Version]