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Convergence Rates for Learning Linear Operators from Noisy Data

27 August 2021

Papers citing "Convergence Rates for Learning Linear Operators from Noisy Data"

42 / 42 papers shown

Title
Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective Simone Brivio Nicola Rares Franco 53 0 0 13 Jun 2025
Learning Where to Learn: Training Distribution Selection for Provable OOD Performance Nicolas Guerra Nicholas H. Nelsen Yunan Yang OOD 156 0 0 27 May 2025
Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization Yash Patel Unique Subedi Ambuj Tewari 100 0 0 23 May 2025
Learning Dual-Arm Coordination for Grasping Large Flat Objects Yongliang Wang Hamidreza Kasaei 130 0 0 04 Apr 2025
Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling Adrienne M. Propp Daniel M. Tartakovsky AI4CE 113 3 0 16 Oct 2024
Structure-Preserving Operator Learning Nacime Bouziani Nicolas Boullé 107 2 0 01 Oct 2024
Operator Learning Using Random Features: A Tool for Scientific Computing Nicholas H. Nelsen Andrew M. Stuart 145 16 0 12 Aug 2024
Optimal Estimation of Structured Covariance Operators Omar Al Ghattas Jiaheng Chen D. Sanz-Alonso Nathan Waniorek 134 5 0 04 Aug 2024
On the estimation rate of Bayesian PINN for inverse problems Yi Sun Debarghya Mukherjee Yves Atchadé PINN 132 1 0 21 Jun 2024
Covariance Operator Estimation via Adaptive Thresholding Omar Al Ghattas D. Sanz-Alonso 134 3 0 28 May 2024
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows Shuhao Cao Francesco Brarda Ruipeng Li Yuanzhe Xi 150 5 0 27 May 2024
MODNO: Multi Operator Learning With Distributed Neural Operators Zecheng Zhang 200 10 0 03 Apr 2024
Operator Learning: Algorithms and Analysis Nikola B. Kovachki S. Lanthaler Andrew M. Stuart 188 47 0 24 Feb 2024
Spectrally Transformed Kernel Regression Runtian Zhai Rattana Pukdee Roger Jin Maria-Florina Balcan Pradeep Ravikumar BDL 97 2 0 01 Feb 2024
Operator learning without the adjoint Nicolas Boullé Diana Halikias Samuel E. Otto Alex Townsend 65 5 0 31 Jan 2024
Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems Giovanni S. Alberti Luca Ratti Matteo Santacesaria Silvia Sciutto 83 1 0 29 Jan 2024
Nonlinear functional regression by functional deep neural network with kernel embedding Zhongjie Shi Jun Fan Linhao Song Ding-Xuan Zhou Johan A. K. Suykens 563 5 0 05 Jan 2024
Operator learning for hyperbolic partial differential equations Christopher Wang Alex Townsend 124 4 0 29 Dec 2023
A Mathematical Guide to Operator Learning Nicolas Boullé Alex Townsend 129 55 0 22 Dec 2023
Inverse Problems with Learned Forward Operators Simon Arridge Andreas Hauptmann Yury Korolev 114 3 0 21 Nov 2023
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators Zongren Zou Xuhui Meng George Karniadakis AI4CE 124 33 0 19 Nov 2023
Covariance Operator Estimation: Sparsity, Lengthscale, and Ensemble Kalman Filters Omar Al Ghattas Jiaheng Chen D. Sanz-Alonso Nathan Waniorek 113 8 0 25 Oct 2023
Online Infinite-Dimensional Regression: Learning Linear Operators Vinod Raman Unique Subedi Ambuj Tewari 96 1 0 08 Sep 2023
Error Bounds for Learning with Vector-Valued Random Features S. Lanthaler Nicholas H. Nelsen 139 18 0 26 May 2023
Nonlocality and Nonlinearity Implies Universality in Operator Learning S. Lanthaler Zong-Yi Li Andrew M. Stuart 132 19 0 26 Apr 2023
Machine Learning for Partial Differential Equations Steven L. Brunton J. Nathan Kutz AI4CE 124 21 0 30 Mar 2023
Operator learning with PCA-Net: upper and lower complexity bounds S. Lanthaler 158 31 0 28 Mar 2023
Elliptic PDE learning is provably data-efficient N. Boullé Diana Halikias Alex Townsend 156 26 0 24 Feb 2023
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs Ke Chen Chunmei Wang Haizhao Yang AI4CE 110 15 0 28 Jan 2023
Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation Jose Antonio Lara Benitez Takashi Furuya F. Faucher Anastasis Kratsios X. Tricoche Maarten V. de Hoop 199 26 0 27 Jan 2023
A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators Neil K. Chada Quanjun Lang Fei Lu Xiang Wang 94 3 0 29 Dec 2022
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem Mattes Mollenhauer Nicole Mücke T. Sullivan 146 27 0 16 Nov 2022
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 191 113 0 15 Nov 2022
Minimax Optimal Kernel Operator Learning via Multilevel Training Jikai Jin Yiping Lu Jose H. Blanchet Lexing Ying 143 13 0 28 Sep 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 137 9 0 28 May 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 174 9 0 15 May 2022
Learning Green's functions associated with time-dependent partial differential equations N. Boullé Seick Kim Tianyi Shi Alex Townsend AI4CE 146 26 0 27 Apr 2022
On the sample complexity of stabilizing linear dynamical systems from data Steffen W. R. Werner Benjamin Peherstorfer 69 9 0 28 Feb 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 245 46 0 01 Jan 2022
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 90 25 0 14 Dec 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 130 20 0 26 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 130 35 0 13 Jun 2021