Regensburg 2022 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 19: Machine Learning in Dynamics and Statistical Physics (joint session DY/SOE)
SOE 19.3: Vortrag
Freitag, 9. September 2022, 10:30–10:45, H19
Machine Learning the 2D percolation transition — •Djénabou Bayo1,2, Andreas Honecker2, and Rudolf A. Römer1 — 1Departement of Physics, University of Warwick, Coventry, CV47AL, United Kingdom — 2Laboratoire de Physique Théorique et Modélisation (LPTM) (CNRS UMR8089), CY Cergy Paris Université, 95302 Cergy-Pontoise, France
The percolation model is one of the simplest models in statistical physics displaying a phase transition. 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 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 seemingly detect the percolation transition from images of percolation clusters. We employ such supervised learning techniques, i.e., classification and regression for 2D site percolation. We find that the identification of spanning clusters provided by such methods does not fully correlate with their existence. Rather, the identification seems to rely on proxy measures such as the site occupation density. Furthermore, constructing challenging cluster distributions show scope for much misclassification when using even highly trained DL networks. Unsupervised ML strategies, such as variational autoencoders, might be able to reconstruct percolation clusters with acceptable spatial resolution, but in many cases struggle to reproduce the geometry of spanning clusters faithfully. Our work uses Python and the ML/DL libraries of PyTorch.