du 17 juin 2021 au 18 juin 2021
Publié le 17 juin 2021 Mis à jour le 17 juin 2021

Séminaire de Djenabou Bayo


Machine Learning the 2D Percolation Transitions

Jeudi 17 juin, 14h00 (heure de Paris) (en distanciel sur Microsoft Teams) ( Team CY Warwick Theoretical Physics )

Machine Learning the 2D Percolation Transitions

Djenabou BAYO
( Université de Warwick, Theoretical Physics) (LPTM Cergy Paris Université/CNRS)

The percolation model is one of the simplest models in statistical physics displaying a phase transition [1]. A classical lattice is occupied randomly with a given probability at each site (or bond). A phase transition from a non-percolating to a percolating state appears around a probability pc, the so-called percolation threshold. Machine Learning (ML) and Deep Learning (DL) techniques are still relatively new methods when applied to physics. Recent work shows that ML/DL techniques allow to detect phase transitions directly from images of computed quantum states [2,3]. Here, we implement ML/DL techniques to identify the percolation threshold in 2D by identifying the connectivity properties of percolation clusters. We employ a standard image classification strategy with a multi-layered convolutional neural network. In addition, we also work directly with the numerical raw data. The implementation is carried out in Python with the ML/DL libraries of Pytorch [4]. We pay special attention to the question of whether these DL methods can indeed identify percolation, i.e. spanning clusters, or are just counting occupation densities.

[1] D. Stauffer and A. Aharony Introduction to percolation theory, Taylor & Francis (1992).
[2] T. Mano and T. Ohtsuki Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models Using Deep Three-Dimensional Convolutional Neural Network, J. Phys. Soc. Japan 86, 113704 (2017).
[3] T. Mano and T. Ohtsuki Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems, J. Phys. Soc. Japan 85,123706 (2016).
[4] A. Paszke, S. Gross, et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library. (2019).

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