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06/28/2023
The curse of dimensionality in operator learning
Neural operator architectures employ neural networks to approximate oper...
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05/26/2023
Error Bounds for Learning with Vector-Valued Random Features
This paper provides a comprehensive error analysis of learning with vect...
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05/15/2023
Neural Oscillators are Universal
Coupled oscillators are being increasingly used as the basis of machine ...
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04/26/2023
The Nonlocal Neural Operator: Universal Approximation
Neural operator architectures approximate operators between infinite-dim...
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03/28/2023
Operator learning with PCA-Net: upper and lower complexity bounds
PCA-Net is a recently proposed neural operator architecture which combin...
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10/03/2022
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities
A large class of hyperbolic and advection-dominated PDEs can have soluti...
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07/15/2021
On the well-posedness of Bayesian inversion for PDEs with ill-posed forward problems
We study the well-posedness of Bayesian inverse problems for PDEs, for w...
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07/15/2021
On universal approximation and error bounds for Fourier Neural Operators
Fourier neural operators (FNOs) have recently been proposed as an effect...
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04/18/2021
On the approximation of functions by tanh neural networks
We derive bounds on the error, in high-order Sobolev norms, incurred in ...
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02/18/2021
Error estimates for DeepOnets: A deep learning framework in infinite dimensions
DeepOnets have recently been proposed as a framework for learning nonlin...
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04/03/2020
On concentration in vortex sheets
The question of energy concentration in approximate solution sequences u...
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09/14/2019