DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems

31 December 2020

Steven L. Brunton

Papers citing "DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems"

20 / 20 papers shown

Title
An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study Milad Ramezankhani A. Deodhar Rishi Parekh Dagnachew Birru AI4CE 50 3 0 20 Jun 2024
Neural Green's Operators for Parametric Partial Differential Equations Hugo Melchers Joost Prins Michael Abdelmalik 58 3 0 04 Jun 2024
A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains Yusuke Yamazaki Ali Harandi Mayu Muramatsu A. Viardin Markus Apel T. Brepols Stefanie Reese Shahed Rezaei AI4CE 39 12 0 21 May 2024
Operator learning for hyperbolic partial differential equations Christopher Wang Alex Townsend 39 2 0 29 Dec 2023
Error Bounds for Learning with Vector-Valued Random Features S. Lanthaler Nicholas H. Nelsen 27 12 0 26 May 2023
Machine Learning for Partial Differential Equations Steven L. Brunton J. Nathan Kutz AI4CE 45 20 0 30 Mar 2023
Elliptic PDE learning is provably data-efficient N. Boullé Diana Halikias Alex Townsend 25 18 0 24 Feb 2023
Learning PDE Solution Operator for Continuous Modeling of Time-Series Yesom Park Jaemoo Choi Changyeon Yoon Changhoon Song Myung-joo Kang AI4TS AI4CE 27 3 0 02 Feb 2023
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 29 18 0 27 Oct 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 29 6 0 28 May 2022
BI-GreenNet: Learning Green's functions by boundary integral network Guochang Lin Fu-jun Chen Pipi Hu Xiang Chen Junqing Chen Jun Wang Zuoqiang Shi 34 20 0 28 Apr 2022
Learning Green's functions associated with time-dependent partial differential equations N. Boullé Seick Kim Tianyi Shi Alex Townsend AI4CE 29 25 0 27 Apr 2022
How to Understand Masked Autoencoders Shuhao Cao Peng Xu David A. Clifton 29 40 0 08 Feb 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 32 110 0 04 Jan 2022
Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows Hamidreza Eivazi S. L. C. Martínez S. Hoyas Ricardo Vinuesa 33 92 0 03 Sep 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 49 15 0 26 Aug 2021
Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer B. Keith U. Khristenko B. Wohlmuth 25 7 0 23 Jul 2021
Modern Koopman Theory for Dynamical Systems Steven L. Brunton M. Budišić E. Kaiser J. Nathan Kutz AI4CE 46 392 0 24 Feb 2021
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 238 2,298 0 18 Oct 2020
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics C. Wehmeyer Frank Noé AI4CE BDL 111 356 0 30 Oct 2017