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Data-driven latent representations for time-dependent problems - Lecture 1
Multi angle
Authors : Zepeda-Núñez, Leonardo (Author of the conference)
CIRM (Publisher )
65C20 - Models (numerical methods)
65L20 - Stability of numerical methods
37N30 - Dynamical systems in numerical analysis
CIRM (Publisher )
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Abstract :
High-fidelity numerical simulation of physical systems modeled by time-dependent partial differential equations (PDEs) has been at the center of many technological advances in the last century. However, for engineering applications such as design, control, optimization, data assimilation, and uncertainty quantification, which require repeated model evaluation over a potentially large number of parameters, or initial conditions, these simulations remain prohibitively expensive, even with state-of-art PDE solvers. The necessity of reducing the overall cost for such downstream applications has led to the development of surrogate models, which captures the core behavior of the target system but at a fraction of the cost. In this context, new advances in machine learning provide a new path for developing surrogates models, particularly when the PDEs are not known and the system is advection-dominated. In a nutshell, we seek to find a data-driven latent representation of the state of the system, and then learn the latent-space dynamics. This allows us to compress the information, and evolve in compressed form, therefore, accelerating the models. In this series of lectures, I will present recent advances in two fronts: deterministic and probabilistic modeling latent representations. In particular, I will introduce the notions of hyper-networks, a neural network that outputs another neural network, and diffusion models, a framework that allows us to represent probability distributions of trajectories directly. I will provide the foundation for such methodologies, how they can be adapted to scientific computing, and which physical properties they need to satisfy. Finally, I will provide several examples of applications to scientific computing.
Keywords : scientific machine learning; generative methods; sampling; diffusion models; hyper-networks
MSC Codes : Keywords : scientific machine learning; generative methods; sampling; diffusion models; hyper-networks
65C20 - Models (numerical methods)
65L20 - Stability of numerical methods
37N30 - Dynamical systems in numerical analysis
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 04/08/2023 Conference Date : 20/07/2023 Subseries : Research School arXiv category : Machine Learning ; Artificial Intelligence Mathematical Area(s) : Numerical Analysis & Scientific Computing ; Computer Science ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:26:33 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-07-20_Zepeda_Nunez_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.20072203Cite this video as: Zepeda-Núñez, Leonardo (2023). Data-driven latent representations for time-dependent problems - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20072203 URI : http://dx.doi.org/10.24350/CIRM.V.20072203 |
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] Learning operators - Lecture 3 / Author of the conference Mishra, Siddhartha.
- [Multi angle] Learning operators - Lecture 2 / Author of the conference Mishra, Siddhartha.
- [Multi angle] Learning operators - Lecture 1 / 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
- FINZI, Marc Anton, BORAL, Anudhyan, WILSON, Andrew Gordon, et al. User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems. In : International Conference on Machine Learning. PMLR, 2023. p. 10136-10152. - https://proceedings.mlr.press/v202/finzi23a/finzi23a.pdf
- WAN, Zhong Yi, BAPTISTA, Ricardo, CHEN, Yi-fan, et al. Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models. arXiv preprint arXiv:2305.15618, 2023. - https://doi.org/10.48550/arXiv.2305.15618
- BORAL, Anudhyan, WAN, Zhong Yi, ZEPEDA-NÚÑEZ, Leonardo, et al. Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations. arXiv preprint arXiv:2306.01174, 2023. - https://doi.org/10.48550/arXiv.2306.01174
- WAN, Zhong Yi, ZEPEDA-NÚÑEZ, Leonardo, BORAL, Anudhyan, et al. Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems. arXiv preprint arXiv:2301.10391, 2023. - https://doi.org/10.48550/arXiv.2301.10391
- DRESDNER, Gideon, KOCHKOV, Dmitrii, NORGAARD, Peter, et al. Learning to correct spectral methods for simulating turbulent flows. arXiv preprint arXiv:2207.00556, 2022. - https://doi.org/10.48550/arXiv.2207.00556
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