English
Learning operators - Lecture 2
Multi angle
Auteurs : Mishra, Siddhartha (Auteur de la Conférence)
CIRM (Editeur )
65Mxx - Numerical methods for IVP of PDE
65Nxx - Partial differential equations, boundary value problems
68Txx - Artificial intelligence
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : machine learning; operators; neural networks
65Mxx - Numerical methods for IVP of PDE
65Nxx - Partial differential equations, boundary value problems
68Txx - Artificial intelligence
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 04/08/2023 Date de captation : 19/07/2023 Sous collection : Research School arXiv category : Numerical Analysis ; Machine Learning Domaine : Numerical Analysis & Scientific Computing ; Computer Science ; PDE Format : MP4 (.mp4) - HD Durée : 01:33:46 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-07-19_Mishra_2.mp4 
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Informations sur la Rencontre
Nom de la rencontre : CEMRACS 2023: Scientific Machine Learning / CEMRACS 2023: Apprentissage automatique scientifiqueOrganisateurs de la rencontre : Auroux, Didier ; Campos Pinto, Martin ; Després, Bruno ; Dolean, Victorita ; Frénod, Emmanuel ; Lanteri, Stéphane ; Michel-Dansac, Victor Dates : 17/07/2023 - 21/07/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2904.html
Données de citation
DOI : 10.24350/CIRM.V.20071903Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Towards data-driven high fidelity CFD - Lecture 3 / Auteur de la Conférence Beck, Andrea.
- [Multi angle] Towards data-driven high fidelity CFD - Lecture 2 / Auteur de la Conférence Beck, Andrea.
- [Multi angle] Towards data-driven high fidelity CFD - Lecture 1 / Auteur de la Conférence Beck, Andrea.
- [Multi angle] Data-driven latent representations for time-dependent problems - Lecture 3 / Auteur de la Conférence Zepeda-Núñez, Leonardo.
- [Multi angle] Data-driven latent representations for time-dependent problems - Lecture 2 / Auteur de la Conférence Zepeda-Núñez, Leonardo.
- [Multi angle] Data-driven latent representations for time-dependent problems - Lecture 1 / Auteur de la Conférence Zepeda-Núñez, Leonardo.
- [Multi angle] Learning operators - Lecture 1 / Auteur de la Conférence Mishra, Siddhartha.
- [Multi angle] Finite neuron method - Lecture 3 / Auteur de la Conférence Xu, Jinchao.
- [Multi angle] Finite neuron method - Lecture 2 / Auteur de la Conférence Xu, Jinchao.
- [Multi angle] Finite neuron method - Lecture 1 / Auteur de la Conférence Xu, Jinchao.
- [Multi angle] Linear and nonlinear schemes for forward model reduction and inverse problems - Lecture 3 / Auteur de la Conférence Mula Hernandez, Olga.
- [Multi angle] Linear and nonlinear schemes for forward model reduction and inverse problems - Lecture 2 / Auteur de la Conférence Mula Hernandez, Olga.
- [Multi angle] Linear and nonlinear schemes for forward model reduction and inverse problems - Lecture 1 / Auteur de la Conférence Mula Hernandez, Olga.
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