A nonlinear splitting algorithm for systems of partial differential equations with self-diffusion. - Matthew A. Beauregard; Joshua L. Padgett; Rana D. Parshad (J. Comput. Appl. Math., 2017)

Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach. - Joshua L. Padgett; Qin Sheng (Appl. Math. Comput., 2018)

The quenching of solutions to time-space fractional Kawarada problems. - Joshua L. Padgett (Comput. Math. Appl., 2018)

Object classification in analytical chemistry via data-driven discovery of partial differential equations. - Joshua Lee Padgett; Yusup Geldiyev; Sakshi Gautam; Wenjing Peng; Yehia Mechref; Akif I. Ibraguimov (Comput. Math. Methods, 2021)

A series representation of the discrete fractional Laplace operator of arbitrary order. - Tiffany Frugé Jones; Evdokiya Georgieva Kostadinova; Joshua Lee Padgett; Qin Sheng (CoRR, 2021)

A positivity- and monotonicity-preserving nonlinear operator splitting approach for approximating solutions to quenching-combustion semilinear partial differential equations. - Joshua Lee Padgett; Eduardo Servin (CoRR, 2021)

Strong Lp-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations. - Martin Hutzenthaler; Arnulf Jentzen; Benno Kuckuck; Joshua Lee Padgett (CoRR, 2021)

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense. - Julia Ackermann; Arnulf Jentzen; Thomas Kruse; Benno Kuckuck; Joshua Lee Padgett (CoRR, 2023)

Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials. - Shakil Rafi; Joshua Lee Padgett; Ukash Nakarmi (CoRR, 2024)

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations. - Julia Ackermann; Arnulf Jentzen; Benno Kuckuck; Joshua Lee Padgett (CoRR, 2024)