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Learning operators - Lecture 2

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Authors : Mishra, Siddhartha (Author of the conference)
CIRM (Publisher )

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Abstract : Operators are mappings between infinite-dimensional spaces, which arise in the context of differential equations. Learning operators is challenging due to the inherent infinite-dimensional context. In this course, we present different architectures for learning operators from data. These include operator networks such as DeepONets and Neural operators such as Fourier Neural Operators (FNOs) and their variants. We will present theoretical results that show that these architectures learn operators arising from PDEs. A large number of numerical examples will be provided to illustrate them.

Keywords : machine learning; operators; neural networks

MSC Codes :
65Mxx - Numerical methods for IVP of PDE
65Nxx - Partial differential equations, boundary value problems
68Txx - Artificial intelligence

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 04/08/2023
    Conference Date : 19/07/2023
    Subseries : Research School
    arXiv category : Numerical Analysis ; Machine Learning
    Mathematical Area(s) : Numerical Analysis & Scientific Computing ; Computer Science ; PDE
    Format : MP4 (.mp4) - HD
    Video Time : 01:33:46
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2023-07-19_Mishra_2.mp4

Information on the Event

Event Title : CEMRACS 2023: Scientific Machine Learning / CEMRACS 2023: Apprentissage automatique scientifique
Event Organizers : Auroux, Didier ; Campos Pinto, Martin ; Després, Bruno ; Dolean, Victorita ; Frénod, Emmanuel ; Lanteri, Stéphane ; Michel-Dansac, Victor
Dates : 17/07/2023 - 21/07/2023
Event Year : 2023
Event URL : https://conferences.cirm-math.fr/2904.html

Citation Data

DOI : 10.24350/CIRM.V.20071903
Cite this video as: Mishra, Siddhartha (2023). Learning operators - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20071903
URI : http://dx.doi.org/10.24350/CIRM.V.20071903

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