Out-of-Distributional Risk Bounds for Neural Operators with Applications to Thehelmholtz Equation

Jose Antonio Lara Benitez, Takashi Furuya, Florian Faucher, Anastasis Kratsios, Xavier Tricoche, Maarten V. de Hoop

Type: Preprint

Publication Date: 2023-01-01

Citations: 3

DOI: https://doi.org/10.2139/ssrn.4527168

Similar Works

Action	Title	Year	Authors
+	Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation	2023	Jose Antonio Lara Benitez Takashi Furuya Florian Faucher Anastasis Kratsios Xavier Tricoche Maarten V. de Hoop
+ PDF Chat	Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation	2024	Jose Antonio Lara Benitez Takashi Furuya Florian Faucher Anastasis Kratsios Xavier Tricoche Maarten V. de Hoop
+ PDF Chat	Deep learning architectures for nonlinear operator functions and nonlinear inverse problems	2022	Maarten V. de Hoop Matti Lassas Christopher A. Wong
+	Deep learning architectures for nonlinear operator functions and nonlinear inverse problems	2019	Maarten V. de Hoop Matti Lassas Christopher A. Wong
+ PDF Chat	Error estimates for DeepONets: a deep learning framework in infinite dimensions	2022	Samuel Lanthaler Siddhartha Mishra George Em Karniadakis
+ PDF Chat	Operator Learning: Algorithms and Analysis	2024	Nikola B. Kovachki Samuel Lanthaler Andrew M. Stuart
+ PDF Chat	Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves	2024	Claudio Muñoz Nicolás Valenzuela
+	On the Representation of Solutions to Elliptic PDEs in Barron Spaces	2021	Ziang Chen Jianfeng Lu Yulong Lu
+	On the Representation of Solutions to Elliptic PDEs in Barron Spaces	2021	Ziang Chen Jianfeng Lu Yulong Lu
+	Error estimates for DeepOnets: A deep learning framework in infinite dimensions	2021	Samuel Lanthaler Siddhartha Mishra George Em Karniadakis
+ PDF Chat	A Mathematical Analysis of Neural Operator Behaviors	2024	Van Bang Lê Mehmet Di̇k
+ PDF Chat	Approximation Rates in Fr\'echet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers	2024	Ahmed Abdeljawad Thomas Dittrich
+ PDF Chat	A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks	2024	Khemraj Shukla Juan Diego Toscano Zhicheng Wang Zongren Zou George Em Karniadakis
+ PDF Chat	Optimal Convergence Rates for Neural Operators	2024	Mike Nguyen Nicole Mücke
+	Neural Operator: Learning Maps Between Function Spaces.	2021	Nikola B. Kovachki Zongyi Li Burigede Liu Kamyar Azizzadenesheli Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar
+ PDF Chat	DimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning	2024	Yichen Song Yan Wang Xiaokang Yang
+	How Analysis Can Teach Us the Optimal Way to Design Neural Operators	2024	Vu-anh Le Mehmet Di̇k
+ PDF Chat	How Analysis Can Teach Us the Optimal Way to Design Neural Operators	2024	Van Bang Lê Mehmet Di̇k
+	Beyond the Courant-Friedrichs-Lewy condition: Numerical methods for the wave problem using deep learning	2021	Oded Ovadia Adar Kahana Eli Turkel Shai Dekel
+ PDF Chat	Structure-informed operator learning for parabolic Partial Differential Equations	2024	Fred Espen Benth Nils Detering Luca Galimberti

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (0)

Action	Title	Year	Authors