In addition to my published work below, my Google Scholar profile may be found here and my ORCID iD here


 1. Error bounds for learning with vector-valued random features

Samuel Lanthaler and Nicholas H. Nelsen

Accepted as NeurIPS 2023 spotlight. Submitted May 2023.

[arXiv:2305.17170 stat.ML]

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]

 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]

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]


 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


 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. 

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 1. Advanced and exploratory shock sensing mechanisms

Nicholas H. Nelsen et al.

Sandia National Laboratories Technical Report SAND2017-10221, 2017. 

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