CIRM - Videos & books Library - Data-driven latent representations for time-dependent problems

Multi angle

Auteurs : Zepeda-Núñez, Leonardo (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : 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

Codes MSC :
65C20 - Models (numerical methods)
65L20 - Stability of numerical methods
37N30 - Dynamical systems in numerical analysis

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Récanzone, Luca

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https://videos.cirm-math.fr/2023-07-20_Zepeda_Nunez_2.mp4

Informations sur la Rencontre

Nom de la rencontre : CEMRACS 2023: Scientific Machine Learning / CEMRACS 2023: Apprentissage automatique scientifique
Organisateurs 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.20072303
Citer cette vidéo: Zepeda-Núñez, Leonardo (2023). Data-driven latent representations for time-dependent problems - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20072303
URI : http://dx.doi.org/10.24350/CIRM.V.20072303

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 1 / Auteur de la Conférence Zepeda-Núñez, Leonardo.
[Multi angle] Learning operators - Lecture 3 / Auteur de la Conférence Mishra, Siddhartha.
[Multi angle] Learning operators - Lecture 2 / Auteur de la Conférence Mishra, Siddhartha.
[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.
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[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.

Bibliographie

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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