Publications

Preprints

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

Samuel Lanthaler and Nicholas H. Nelsen

Accepted as NeurIPS 2023 spotlight. Submitted May 2023.

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.

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.

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.

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.

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.

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.

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.

1. Advanced and exploratory shock sensing mechanisms

Nicholas H. Nelsen et al.

Sandia National Laboratories Technical Report SAND2017-10221, 2017.