A Mathematical Guide to Operator Learning

Fuente: arXiv
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Bibliographic Details
Main Authors: Boullé, Nicolas, Townsend, Alex
Format: Preprint
Published: 2023
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author Boullé, Nicolas
Townsend, Alex
author_facet Boullé, Nicolas
Townsend, Alex
contents Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable to operator learning, discuss various neural network architectures, and explain how to employ numerical PDE solvers effectively. We also give advice on how to create and manage training data and conduct optimization. We offer intuition behind the various neural network architectures employed in operator learning by motivating them from the point-of-view of numerical linear algebra.
format Preprint
id arxiv_https___arxiv_org_abs_2312_14688
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A Mathematical Guide to Operator Learning
Boullé, Nicolas
Townsend, Alex
Numerical Analysis
Artificial Intelligence
Machine Learning
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable to operator learning, discuss various neural network architectures, and explain how to employ numerical PDE solvers effectively. We also give advice on how to create and manage training data and conduct optimization. We offer intuition behind the various neural network architectures employed in operator learning by motivating them from the point-of-view of numerical linear algebra.
title A Mathematical Guide to Operator Learning
topic Numerical Analysis
Artificial Intelligence
Machine Learning
url https://arxiv.org/abs/2312.14688