SKM 2023 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Machine Learning in Dynamics and Statistical Physics I
DY 17.3: Vortrag
Dienstag, 28. März 2023, 10:30–10:45, ZEU 160
Machine Learning Percolation: Does it understand the physics? — •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 at a critical site occupation probability pc. The hallmark of the percolation transition is the emergence of a spanning cluster of connected neighboring sites across the lattice. Machine learning (ML) approaches to percolation have shown that the non-spanning (p<pc) and the spanning (p>pc) phases can be identified reasonably well with supervised deep learning (DL) strategies for classification based on convolutional neural networks (CNNs). Surprisingly, the role of the spanning cluster seems to be less prominent in such DL methods. Here, we show that CNNs, when trained with the site occupation probabilities p as labels, can classify not only the two phases p<pc and p>pc, but also according to the many individual p’s. Nevertheless, the same CNNs struggle when trying to predict the emergence of the spanning cluster. Indeed, when we train with correlation lengths or the existence of the spanning cluster, the results suggest that the CNNs seem to rely mostly on the p’s as a proxy measure. This suggests that the essential physics of the spanning cluster is not actually what determines the DL results.