Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks

Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks

12 February 2025

David T. Fuentes

Beatrice Riviere

Papers citing "Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks"

17 / 17 papers shown

Title
Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networks A. Celaya Keegan L. A. Kirk David T. Fuentes Beatrice Riviere 37 1 0 01 Nov 2023
Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility Jochen Stiasny Spyros Chatzivasileiadis PINN AI4CE 50 11 0 15 Mar 2023
Graph Neural Network-based Surrogate Models for Finite Element Analysis Meduri Venkata Shivaditya J. Alves Francesca Bugiotti Frédéric Magoulès AI4CE 38 5 0 17 Nov 2022
Inversion of Time-Lapse Surface Gravity Data for Detection of 3D CO $_2$ Plumes via Deep Learning A. Celaya B. Denel Yen Sun Mauricio Araya-Polo A. Price 3DPC 52 11 0 06 Sep 2022
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks Chen-Chun Wu Min Zhu Qinyan Tan Yadhu Kartha Lu Lu 67 372 0 21 Jul 2022
CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method P. Chiu Jian Cheng Wong C. Ooi M. Dao Yew-Soon Ong PINN 48 213 0 29 Oct 2021
An extended physics informed neural network for preliminary analysis of parametric optimal control problems N. Demo M. Strazzullo G. Rozza PINN 46 34 0 26 Oct 2021
Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data Xiaoyu Zhao Zhiqiang Gong Yunyang Zhang Wen Yao Xiaoqian Chen OOD AI4CE 111 94 0 26 Sep 2021
PocketNet: A Smaller Neural Network for Medical Image Analysis A. Celaya Jonas A. Actor Rajarajesawari Muthusivarajan Evan Gates C. Chung Dawid Schellingerhout B. Rivière David T. Fuentes SSeg MedIm 32 27 0 21 Apr 2021
The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers? Stefano Markidis PINN 60 188 0 12 Mar 2021
$Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms$ Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms Ingo Gühring Gitta Kutyniok P. Petersen 76 199 0 21 Feb 2019
MobileNetV2: Inverted Residuals and Linear Bottlenecks Mark Sandler Andrew G. Howard Menglong Zhu A. Zhmoginov Liang-Chieh Chen 173 19,262 0 13 Jan 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
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 91 2,060 0 24 Aug 2017
MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications Andrew G. Howard Menglong Zhu Bo Chen Dmitry Kalenichenko Weijun Wang Tobias Weyand M. Andreetto Hartwig Adam 3DH 1.1K 20,832 0 17 Apr 2017
U-Net: Convolutional Networks for Biomedical Image Segmentation Olaf Ronneberger Philipp Fischer Thomas Brox SSeg 3DV 1.8K 77,099 0 18 May 2015