Neural Operator: Learning Maps Between Function Spaces

19 August 2021

Nikola B. Kovachki

Zong-Yi Li

Burigede Liu

Kamyar Azizzadenesheli

Papers citing "Neural Operator: Learning Maps Between Function Spaces"

33 / 283 papers shown

Title
Applications of physics informed neural operators S. Rosofsky Hani Al Majed Eliu A. Huerta PINN AI4CE 22 39 0 23 Mar 2022
Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling Huaiqian You Quinn Zhang Colton J. Ross Chung-Hao Lee Yue Yu AI4CE 21 95 0 15 Mar 2022
Local neural operator for solving transient partial differential equations on varied domains Hongyu Li Ximeng Ye Pengjie Jiang G. Qin Tiejun Wang AI4CE 6 6 0 11 Mar 2022
Data adaptive RKHS Tikhonov regularization for learning kernels in operators Fei Lu Quanjun Lang Qi An 22 12 0 08 Mar 2022
Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors Yibo Yang Georgios Kissas P. Perdikaris BDL UQCV 32 40 0 06 Mar 2022
Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations Joan Bruna Benjamin Peherstorfer Eric Vanden-Eijnden 19 60 0 02 Mar 2022
Learning Neural Hamiltonian Dynamics: A Methodological Overview Zhijie Chen Mingquan Feng Junchi Yan H. Zha AI4CE 19 15 0 28 Feb 2022
Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems Minglang Yin Enrui Zhang Yue Yu George Karniadakis AI4CE 30 99 0 25 Feb 2022
Learning Stochastic Dynamics with Statistics-Informed Neural Network Yuanran Zhu Yunhao Tang Changho Kim 19 18 0 24 Feb 2022
Learning continuous models for continuous physics Aditi S. Krishnapriyan A. Queiruga N. Benjamin Erichson Michael W. Mahoney AI4CE 24 33 0 17 Feb 2022
Local approximation of operators H. Mhaskar 11 8 0 13 Feb 2022
MIONet: Learning multiple-input operators via tensor product Pengzhan Jin Shuai Meng Lu Lu 20 158 0 12 Feb 2022
Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach Evangelos Galaris Gianluca Fabiani I. Gallos Ioannis G. Kevrekidis Constantinos Siettos AI4CE 23 40 0 31 Jan 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 29 110 0 04 Jan 2022
Frame invariance and scalability of neural operators for partial differential equations M. Zafar Jiequn Han Xueqing Zhou Heng Xiao 16 5 0 28 Dec 2021
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations C. Marcati Christoph Schwab 16 38 0 15 Dec 2021
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks Thomas O'Leary-Roseberry Xiaosong Du A. Chaudhuri J. Martins Karen E. Willcox Omar Ghattas 30 22 0 14 Dec 2021
Data-driven modelling of nonlinear dynamics by barycentric coordinates and memory Niklas Wulkow P. Koltai V. Sunkara Christof Schütte 24 3 0 13 Dec 2021
Factorized Fourier Neural Operators Alasdair Tran A. Mathews Lexing Xie Cheng Soon Ong AI4CE 31 142 0 27 Nov 2021
Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers John Guibas Morteza Mardani Zong-Yi Li Andrew Tao Anima Anandkumar Bryan Catanzaro 21 229 0 24 Nov 2021
Residual fourier neural operator for thermochemical curing of composites Gengxiang Chen Yingguang Li Xu Liu Qinglu Meng Jing Zhou Xiaozhong Hao AI4CE 14 7 0 15 Nov 2021
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 62 384 0 06 Nov 2021
Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs Guang Lin Christian Moya Zecheng Zhang 15 30 0 03 Nov 2021
Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics C. Salvi M. Lemercier A. Gerasimovičs AI4CE 21 42 0 19 Oct 2021
Improved architectures and training algorithms for deep operator networks Sizhuang He Hanwen Wang P. Perdikaris AI4CE 49 105 0 04 Oct 2021
Scale-invariant Learning by Physics Inversion Philipp Holl V. Koltun Nils Thuerey PINN AI4CE 21 8 0 30 Sep 2021
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks Annan Yu Chloe Becquey Diana Halikias Matthew Esmaili Mallory Alex Townsend 59 8 0 23 Sep 2021
Convergence Rates for Learning Linear Operators from Noisy Data Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart 19 54 0 27 Aug 2021
Learning Dissipative Dynamics in Chaotic Systems Zong-Yi Li Miguel Liu-Schiaffini Nikola B. Kovachki Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 23 25 0 13 Jun 2021
Learning the optimal Tikhonov regularizer for inverse problems Giovanni S. Alberti E. De Vito Matti Lassas Luca Ratti Matteo Santacesaria 25 30 0 11 Jun 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 223 2,287 0 18 Oct 2020
MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework C. Jiang S. Esmaeilzadeh Kamyar Azizzadenesheli K. Kashinath Mustafa A. Mustafa H. Tchelepi P. Marcus P. Prabhat Anima Anandkumar AI4CE 187 141 0 01 May 2020
Sharp analysis of low-rank kernel matrix approximations Francis R. Bach 86 277 0 09 Aug 2012