Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces

1 January 2022

Papers citing "Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces"

22 / 22 papers shown

Title
Nonlinear functional regression by functional deep neural network with kernel embedding Zhongjie Shi Jun Fan Linhao Song Ding-Xuan Zhou Johan A. K. Suykens 446 5 0 05 Jan 2024
Stationary Density Estimation of Itô Diffusions Using Deep Learning Yiqi Gu J. Harlim Senwei Liang Haizhao Yang 46 12 0 09 Sep 2021
Convergence Rates for Learning Linear Operators from Noisy Data Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart 156 57 0 27 Aug 2021
Elementary superexpressive activations Dmitry Yarotsky 56 35 0 22 Feb 2021
Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$ -widths of Shallow Neural Networks Jonathan W. Siegel Jinchao Xu 111 87 0 29 Jan 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 47 37 0 05 Jan 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 480 2,397 0 18 Oct 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 57 173 0 29 Jun 2020
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory Yaoyu Zhang Haizhao Yang 48 75 0 28 Jun 2020
Neural Operator: Graph Kernel Network for Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar 181 732 0 07 Mar 2020
Deep Network Approximation for Smooth Functions Jianfeng Lu Zuowei Shen Haizhao Yang Shijun Zhang 97 247 0 09 Jan 2020
Deep Learning on Image Denoising: An overview Chunwei Tian Lunke Fei Wenxian Zheng Yong-mei Xu W. Zuo Chia-Wen Lin 190 829 0 31 Dec 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 220 2,119 0 08 Oct 2019
Learning to Synthesize: Robust Phase Retrieval at Low Photon counts Mo Deng Shuai Li A. Goy Iksung Kang George Barbastathis 162 69 0 26 Jul 2019
Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks Yuan Cao Quanquan Gu MLT AI4CE 80 389 0 30 May 2019
SwitchNet: a neural network model for forward and inverse scattering problems Y. Khoo Lexing Ying 170 134 0 23 Oct 2018
Deep Neural Networks for Estimation and Inference M. Farrell Tengyuan Liang S. Misra BDL 164 254 0 26 Sep 2018
Optimal approximation of continuous functions by very deep ReLU networks Dmitry Yarotsky 176 293 0 10 Feb 2018
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification Yinhao Zhu N. Zabaras UQCV BDL 94 642 0 21 Jan 2018
Nonparametric regression using deep neural networks with ReLU activation function Johannes Schmidt-Hieber 218 810 0 22 Aug 2017
Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks Peter L. Bartlett Nick Harvey Christopher Liaw Abbas Mehrabian 199 431 0 08 Mar 2017
Provable approximation properties for deep neural networks Uri Shaham A. Cloninger Ronald R. Coifman 151 231 0 24 Sep 2015