ICML 2024 Tutorial'Machine Learning on Function spaces #NeuralOperators'

ICML 2024 Tutorial

"Machine Learning on Function spaces #NeuralOperators"

Abstract:
This tutorial will introduce neural operators, an extension of neural networks designed to learn mappings between infinite-dimensional function spaces. We'll cover the theoretical foundations, including their formulation and universal approximation capabilities. Emphasizing their discretization-invariance, we'll explore how neural operators tackle problems in partial differential equations (PDEs) and scientific computing tasks. This session is ideal for machine learning experts looking to leverage neural operators for advanced scientific and engineering applications.

You may find the relevant
papers:
Neural Operator: Graph Kernel Network for Partial Differential Equations

Multipole Graph Neural Operator for Parametric Partial Differential Equations

Fourier Neural Operator for Parametric Partial Differential Equations

Markov Neural Operators for Learning Chaotic Systems

Neural Operator: Learning Maps Between Function Spaces

Physics-Informed Neural Operator for Learning Partial Differential Equations

U-NO: U-shaped Neural Operators

Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs

Geometry-Informed Neural Operator for Large-Scale 3D PDEs

Blog posts:

[Yuan-HengWang]

Excellent, thanks for sharing! Adding new learning task into my list.

[jesusmtz]

Do you have a ref to a proof of the statement at 21:32? Great talk

[abhijeetvyas]

Insightful talk - 37:31 is classic for Fourier basis.

[themosst]

Thanks for the video. At 30:00 you switch from a(x) to a(y) in the integral. Is this an error?

[TG-bfum]

Is there a version of this tutorial where the video slides are visible?

[alirezamogharabi]

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