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"

44 / 44 papers shown

Title
Interpretability and Generalization Bounds for Learning Spatial Physics Alejandro Francisco Queiruga Theo Gutman-Solo Shuai Jiang AI4CE 28 0 0 18 Jun 2025
Learning Dual-Arm Coordination for Grasping Large Flat Objects Yongliang Wang Hamidreza Kasaei 92 0 0 04 Apr 2025
Orthogonal greedy algorithm for linear operator learning with shallow neural network Ye Lin Jiwei Jia Young Ju Lee Ran Zhang 78 1 0 06 Jan 2025
An explainable operator approximation framework under the guideline of Green's function Jianghang Gu Ling Wen Yuntian Chen Shiyi Chen 125 0 0 21 Dec 2024
Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics? Tae-Geun Kim Seong Chan Park 97 0 0 28 Oct 2024
Network scaling and scale-driven loss balancing for intelligent poroelastography Yang Xu Fatemeh Pourahmadian AI4CE 96 1 0 27 Oct 2024
Operator Learning Using Random Features: A Tool for Scientific Computing Nicholas H. Nelsen Andrew M. Stuart 101 14 0 12 Aug 2024
Green Multigrid Network Ye Lin Young Ju Lee Jiwei Jia 74 1 0 04 Jul 2024
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 81 6 0 20 Jun 2024
Neural Green's Operators for Parametric Partial Differential Equations Hugo Melchers Joost Prins Michael Abdelmalik 183 4 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 100 14 0 21 May 2024
A Hybrid Kernel-Free Boundary Integral Method with Operator Learning for Solving Parametric Partial Differential Equations In Complex Domains Shuo Ling Liwei Tan Wenjun Ying 51 0 0 23 Apr 2024
Approximation of RKHS Functionals by Neural Networks Tiancong Zhou Namjoon Suh Guang Cheng Xiaoming Huo 66 4 0 18 Mar 2024
Operator Learning: Algorithms and Analysis Nikola B. Kovachki S. Lanthaler Andrew M. Stuart 148 33 0 24 Feb 2024
Operator learning for hyperbolic partial differential equations Christopher Wang Alex Townsend 83 3 0 29 Dec 2023
A Mathematical Guide to Operator Learning Nicolas Boullé Alex Townsend 93 47 0 22 Dec 2023
Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data R. Stephany Christopher Earls 59 4 0 09 Sep 2023
Interpreting and generalizing deep learning in physics-based problems with functional linear models Amirhossein Arzani Lingxiao Yuan P. Newell Bei Wang AI4CE 80 8 0 10 Jul 2023
NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data Songming Liu Zhongkai Hao Chengyang Ying Hang Su Ze Cheng Jun Zhu AI4CE 65 12 0 30 May 2023
Error Bounds for Learning with Vector-Valued Random Features S. Lanthaler Nicholas H. Nelsen 86 16 0 26 May 2023
Kernel Methods are Competitive for Operator Learning Pau Batlle Matthieu Darcy Bamdad Hosseini H. Owhadi 98 41 0 26 Apr 2023
Machine Learning for Partial Differential Equations Steven L. Brunton J. Nathan Kutz AI4CE 101 21 0 30 Mar 2023
Elliptic PDE learning is provably data-efficient N. Boullé Diana Halikias Alex Townsend 79 21 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 36 3 0 02 Feb 2023
TransNet: Transferable Neural Networks for Partial Differential Equations Zezhong Zhang F. Bao L. Ju Guannan Zhang 74 3 0 27 Jan 2023
BINN: A deep learning approach for computational mechanics problems based on boundary integral equations Jia Sun Yinghua Liu Yizheng Wang Z. Yao Xiao-ping Zheng PINN AI4CE 50 25 0 11 Jan 2023
Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications Zhongkai Hao Songming Liu Yichi Zhang Chengyang Ying Yao Feng Hang Su Jun Zhu PINN AI4CE 127 99 0 15 Nov 2022
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 77 21 0 27 Oct 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 93 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 62 22 0 28 Apr 2022
Learning Green's functions associated with time-dependent partial differential equations N. Boullé Seick Kim Tianyi Shi Alex Townsend AI4CE 97 26 0 27 Apr 2022
SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability Simone Venturi T. Casey 138 42 0 27 Apr 2022
Data adaptive RKHS Tikhonov regularization for learning kernels in operators Fei Lu Quanjun Lang Qi An 57 12 0 08 Mar 2022
How to Understand Masked Autoencoders Shuhao Cao Peng Xu David Clifton 91 42 0 08 Feb 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 86 113 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 89 96 0 03 Sep 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 95 19 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 55 7 0 23 Jul 2021
Operator Autoencoders: Learning Physical Operations on Encoded Molecular Graphs Willis Hoke D. Shea S. Casey AI4CE 52 0 0 26 May 2021
Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver Yuankai Teng Xiaoping Zhang Zhu Wang L. Ju 90 14 0 23 May 2021
Data-driven discovery of Green's functions with human-understandable deep learning Nicolas Boullé Christopher Earls Alex Townsend PINN AI4CE 60 60 0 01 May 2021
Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids Xueqing Zhou Jiequn Han Heng Xiao 78 31 0 11 Mar 2021
Modern Koopman Theory for Dynamical Systems Steven L. Brunton M. Budišić E. Kaiser J. Nathan Kutz AI4CE 133 421 0 24 Feb 2021
Learning elliptic partial differential equations with randomized linear algebra Nicolas Boullé Alex Townsend 50 43 0 31 Jan 2021