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Learning operators - Lecture 1
Multi angle
Authors : Mishra, Siddhartha (Author of the conference)
CIRM (Publisher )
65Mxx - Numerical methods for IVP of PDE
65Nxx - Partial differential equations, boundary value problems
68Txx - Artificial intelligence
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 : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : 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 : 01:19:23 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-07-19_Mishra_1.mp4 
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Information on the Event
Event Title : CEMRACS 2023: Scientific Machine Learning / CEMRACS 2023: Apprentissage automatique scientifiqueEvent 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.20071803Cite this video as: Mishra, Siddhartha (2023). Learning operators - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20071803 URI : http://dx.doi.org/10.24350/CIRM.V.20071803 |
See Also
- [Multi angle] Towards data-driven high fidelity CFD - Lecture 3 / Author of the conference Beck, Andrea.
- [Multi angle] Towards data-driven high fidelity CFD - Lecture 2 / Author of the conference Beck, Andrea.
- [Multi angle] Towards data-driven high fidelity CFD - Lecture 1 / Author of the conference Beck, Andrea.
- [Multi angle] Data-driven latent representations for time-dependent problems - Lecture 3 / Author of the conference Zepeda-Núñez, Leonardo.
- [Multi angle] Data-driven latent representations for time-dependent problems - Lecture 2 / Author of the conference Zepeda-Núñez, Leonardo.
- [Multi angle] Data-driven latent representations for time-dependent problems - Lecture 1 / Author of the conference Zepeda-Núñez, Leonardo.
- [Multi angle] Learning operators - Lecture 3 / Author of the conference Mishra, Siddhartha.
- [Multi angle] Learning operators - Lecture 2 / Author of the conference Mishra, Siddhartha.
- [Multi angle] Finite neuron method - Lecture 3 / Author of the conference Xu, Jinchao.
- [Multi angle] Finite neuron method - Lecture 2 / Author of the conference Xu, Jinchao.
- [Multi angle] Finite neuron method - Lecture 1 / Author of the conference Xu, Jinchao.
- [Multi angle] Linear and nonlinear schemes for forward model reduction and inverse problems - Lecture 3 / Author of the conference Mula Hernandez, Olga.
- [Multi angle] Linear and nonlinear schemes for forward model reduction and inverse problems - Lecture 2 / Author of the conference Mula Hernandez, Olga.
- [Multi angle] Linear and nonlinear schemes for forward model reduction and inverse problems - Lecture 1 / Author of the conference Mula Hernandez, Olga.
Bibliography
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