Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification

18 January 2021

Papers citing "Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification"

12 / 12 papers shown

Title
Physics Informed Neural Networks for Simulating Radiative Transfer Siddhartha Mishra Roberto Molinaro PINN 65 109 0 25 Sep 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 72 83 0 25 Apr 2020
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs S. Fresca Luca Dede' Andrea Manzoni AI4CE 59 262 0 12 Jan 2020
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 182 1,377 0 27 Aug 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 95 1,525 0 10 Jul 2019
Nonlinear Approximation and (Deep) ReLU Networks Ingrid Daubechies Ronald A. DeVore S. Foucart Boris Hanin G. Petrova 100 141 0 05 May 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 63 198 0 31 Mar 2019
Data-driven discovery of PDEs in complex datasets Jens Berg K. Nystrom AI4CE PINN 46 141 0 31 Aug 2018
Optimal approximation of continuous functions by very deep ReLU networks Dmitry Yarotsky 176 293 0 10 Feb 2018
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification Rohit Tripathy Ilias Bilionis AI4CE 60 408 0 02 Feb 2018
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 75 924 0 28 Nov 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 117 1,384 0 30 Sep 2017