Numerical Solution of the Parametric Diffusion Equation by Deep Neural
Networks

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

25 April 2020

Papers citing "Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks"

12 / 12 papers shown

Title
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation Janina Enrica Schutte Martin Eigel AI4CE 27 2 0 19 Mar 2024
Operator theory, kernels, and Feedforward Neural Networks P. Jorgensen Myung-Sin Song James Tian 35 0 0 03 Jan 2023
Multigrid-augmented deep learning preconditioners for the Helmholtz equation Yael Azulay Eran Treister AI4CE 14 30 0 14 Mar 2022
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 18 45 0 10 Mar 2021
Partition of unity networks: deep hp-approximation Kookjin Lee N. Trask Ravi G. Patel Mamikon A. Gulian E. Cyr 14 30 0 27 Jan 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 34 29 0 11 Dec 2020
Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems Donsub Rim Luca Venturi Joan Bruna Benjamin Peherstorfer 15 9 0 28 Jul 2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions Philipp Grohs L. Herrmann 16 52 0 10 Jul 2020
Deep neural network solution of the electronic Schrödinger equation J. Hermann Zeno Schätzle Frank Noé 149 446 0 16 Sep 2019
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications E. Samaniego C. Anitescu S. Goswami Vien Minh Nguyen-Thanh Hongwei Guo Khader M. Hamdia Timon Rabczuk X. Zhuang PINN AI4CE 150 1,339 0 27 Aug 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 17 197 0 31 Mar 2019