Machine learning phases of active matter: Finite size scaling in the Vicsek model by means of a Principle Component Analysis and Neural Networks

Abstract

The interest in understanding the group motion of living systems provides a breeding ground for a plethora of active matter models in statistical physics. The Vicsek model (VM), a minimal model of self-propelled particles in which their tendency to align with each other competes with perturbations controlled by a noise term, captures this behaviour of collective motion. In this thesis the machine learning tools Principal Component Analysis (PCA) and Neural Networks (NN) have been used to detect order-disorder phase transitions in the VM. PCA was able to construct an order parameter even in the presence of limited and inherently noisy data. The NN detected critical points of phase transitions for systems greater than 1000 particles, but struggled to find phase transitions in smaller systems. The finite size scaling found the critical noise value ηc(∞) = 2.11±0.25 without the use of a NN and ηc(∞) = 2.28 ± 0.16 with the use of a NN. Furthermore, critical exponents β = 0.3, γ = 2.1 and ν = 0.9 were extracted.