Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials

1 code implementation • 1 Feb 2024 • Shakil Rafi, Joshua Lee Padgett, Ukash Nakarmi

We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}.

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 $L^p$-sense

no code implementations • 24 Sep 2023 • Julia Ackermann, Arnulf Jentzen, Thomas Kruse, Benno Kuckuck, Joshua Lee Padgett

Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed.

A series representation of the discrete fractional Laplace operator of arbitrary order

no code implementations • 10 Jan 2021 • Tiffany Frugé Jones, Evdokiya Georgieva Kostadinova, Joshua Lee Padgett, Qin Sheng

A series representation of the discrete fractional Laplace operator for positive non-integer powers is developed.

Classical Analysis and ODEs Numerical Analysis Numerical Analysis