23 citations · 127 across the 19 of their papers we have counts for
20 papers
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 +1
It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer…
Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials
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}. Our aim will be to show that,…
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 -sense
Julia Ackermann, Arnulf Jentzen, Thomas Kruse +2
Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have gener…
Strong -error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations
Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck +1
Full-history recursive multilevel Picard (MLP) approximation schemes have been shown to overcome the curse of dimensionality in the numerical approximation of high-dimensional semi…
A positivity- and monotonicity-preserving nonlinear operator splitting approach for approximating solutions to quenching-combustion semilinear partial differential equations
Joshua Lee Padgett, Eduardo Servin
In recent years, there has been a large increase in interest in numerical algorithms which preserve various qualitative features of the original continuous problem. Herein, we prop…
Fractional Laplacian Spectral Approach to Turbulence in a Dusty Plasma Monolayer
Evdokiya G Kostadinova, Rahul Banka, Joshua L Padgett +3
This work presents an analytical investigation of anomalous diffusion and turbulence in a dusty plasma monolayer, where energy transport across scales leads to the spontaneous form…