A unified deep artificial neural network approach to partial differential equations in complex geometries

Jens Berg, Kaj Nyström

Type: Article

Publication Date: 2018-08-23

Citations: 518

DOI: https://doi.org/10.1016/j.neucom.2018.06.056

View Publication

Download PDF

Locations

arXiv (Cornell University) - View - PDF
DataCite API - View
Neurocomputing - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Deep neural network modeling of unknown partial differential equations in nodal space	2021	Zhen Chen Victor Churchill Kailiang Wu Dongbin Xiu
+	Partial Differential Equations Meet Deep Neural Networks: A Survey	2022	Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv
+	Deep learning-based numerical methods for partial differential equations	2020	Yao Dou
+ PDF Chat	Deep Neural Networks Motivated by Partial Differential Equations	2019	Lars Ruthotto Eldad Haber
+ PDF Chat	A derivative-free method for solving elliptic partial differential equations with deep neural networks	2020	Jihun Han Mihai Nica Adam R. Stinchcombe
+	DGM: A deep learning algorithm for solving partial differential equations	2018	Justin Sirignano Konstantinos Spiliopoulos
+	An Overview on Deep Learning Techniques in Solving Partial Differential Equations	2022	Rabiu Bashir Yunus Samsul Ariffin Abdul Karim Afza Shafie Muhammad Izzatullah Ahmed Kherd Mohammad Khatim Hasan Jumat Sulaiman
+	Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations	2022	Wei Wu Xinlong Feng Hui Xu
+	A non-gradient method for solving elliptic partial differential equations with deep neural networks	2022	Yifan Peng Dan Hu Zin-Qin John Xu
+	Deep learning-based method coupled with small sample learning for solving partial differential equations	2020	Ying Li Fangjun Mei
+ PDF Chat	Artificial intelligence for partial differential equations in computational mechanics: A review	2024	Yizheng Wang Jinshuai Bai Zhongya Lin Qimin Wang Cosmin Anitescu Jia Sun Mohammad Sadegh Es-haghi Yuantong Gu Xi‐Qiao Feng Xiaoying Zhuang
+	A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks	2023	Hyeonjung Jung Jayant Gupta Bharat Jayaprakash Matthew Eagon Harish Panneer Selvam Carl Molnar William F. Northrop Shashi Shekhar
+ PDF Chat	Learning Partial Differential Equations with Deep Parallel Neural Operators	2024	Qinglong Ma Peizhi Zhao Sen Wang Tao Song
+	A comparison of deep learning-based techniques for solving partial differential equations	2024	Rabiu Bashir Yunus Nooraini Zainuddin Afza Shafie Muhammad Izzatullah Samsul Ariffin Abdul Karim
+	Numerical Solution of First and Second Order Differential Equations with Deep Neural Networks	2023	Tekumudi Vivek Sai Surya Chaitanya R Prasanna Kumar Dharminder Chaudhary Soumyendra Singh Pratik Shrivastav Dinesh Yadav
+	Deep Neural Network Approach to Forward-Inverse Problems	2019	Hyeontae Jo Hwijae Son Hyung Ju Hwang Eunheui Kim
+	Deep learning algorithms for solving differential equations: a survey	2023	Harender Kumar Neha Yadav
+	Numerical Experiments on a Deep Learning Approach to Solving High- Dimensional Partial Differential Equations	2020	Maria Rebecca Rothe
+ PDF Chat	Deep neural network approach to forward-inverse problems	2020	Hyeontae Jo Hwijae Son Hyung Ju Hwang Eun Heui Kim
+	A Deep Learning Neural Network Framework for Solving Singular Nonlinear Ordinary Differential Equations	2023	Pavithra Venkatachalapathy S. M. Mallikarjunaiah

Works That Cite This (287)

Action	Title	Year	Authors
+ PDF Chat	DeepReach: A Deep Learning Approach to High-Dimensional Reachability	2021	Somil Bansal Claire J. Tomlin
+ PDF Chat	SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs	2021	Amuthan Arunkumar Ramabathiran Prabhu Ramachandran
+ PDF Chat	Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients	2021	Francesco Calabrò Gianluca Fabiani Constantinos Siettos
+ PDF Chat	Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions	2024	Xian Li Jiaxin Deng Jinran Wu Shaotong Zhang Weide Li You‐Gan Wang
+ PDF Chat	Enhanced physics-informed neural networks with Augmented Lagrangian relaxation method (AL-PINNs)	2023	Hwijae Son Sung Woong Cho Hyung Ju Hwang
+	Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC	2021	M.A. Miller R.M. Churchill Alp Dener C. S. Chang Todd Munson R. Hager
+ PDF Chat	WarpPINN: Cine-MR image registration with physics-informed neural networks	2023	Pablo Arratia Hernán Mella Sergio Uribe Daniel E. Hurtado Francisco Sahli Costabal
+	Neural control of discrete weak formulations: Galerkin, least squares & minimal-residual methods with quasi-optimal weights	2022	Ignacio Brevis Ignacio Muga Kristoffer G. van der Zee
+ PDF Chat	The deep minimizing movement scheme	2023	Min Sue Park Cheolhyeong Kim Hwijae Son Hyung Ju Hwang
+ PDF Chat	Two-layer neural networks for partial differential equations: optimization and generalization theory	2024	Tao Luo Haizhao Yang

Works Cited by This (18)

Action	Title	Year	Authors
+	Neural Network Methods for Solving Differential Equations	2015	Neha Yadav Anupam Yadav Manoj Kumar
+	Computational Investigation of Low-Discrepancy Sequences in Simulation Algorithms for Bayesian Networks	2000	J.-J. Cheng Marek J. Drużdżel
+	Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (2000)	2013	Craig Boutilier Moisés Goldszmidt
+ PDF Chat	A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations	2013	Keith Rudd Gianluca Di Muro Silvio Ferrari
+	Remark on algorithm 659	2003	Stephen Joe Frances Y. Kuo
+	Initial boundary value problems for hyperbolic systems	1970	Heinz‐Otto Kreiss
+	Low discrepancy sequences in high dimensions: How well are their projections distributed?	2007	Xiaoqun Wang Ian H. Sloan
+	A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks	2014	Keith Rudd Silvio Ferrari
+	Practical Methods of Optimization	2009	R. Ian Fletcher
+ PDF Chat	Constructing Sobol Sequences with Better Two-Dimensional Projections	2008	Stephen Joe Frances Y. Kuo