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

Submitted May 2023.

[arXiv:2305.17170 stat.ML]

Journal Articles

 3. 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]

 2. 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]

 1. 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]

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


 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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