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DeepOnet - Learning Nonlinear Operators Based on the Universal Approximation Theorem of Operators
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- 1 Introduction
- 2 Universal approximation theorem
- 3 Why is it different
- 4 Classification problem
- 5 New concepts
- 6 Theorem
- 7 Smoothness
- 8 What is a pin
- 9 Autonomy
- 10 Hidden Fluid Mechanics
- 11 Espresso
- 12 Brain Aneurysm
- 13 Operators
- 14 Problem setup
- 15 The universal approximation theorem
- 16 Crossproduct
- 17 Deep Neural Network
- 18 Input Space
- 19 Recap
- 20 Example
- 21 Results
- 22 Learning fractional operators
- 23 Individual trajectories
- 24 Nonlinearity
- 25 Multiphysics
- 26 Eminem
- 27 Spectral Methods
- 28 Can we bound the error in term of the operator norm
- 29 Can we move away from compactness assumption
- 30 What allows these networks to approximate exact solutions
- 31 Can it learn complex userdefined operators
- 32 Wavelets instead of sigmoids
- 33 Variational pins
- 34 Comparing to real neurons
- 35 How to test this idea
