Correlations in the shear flow of athermal amorphous solids: A principal component analysis

Machine learning methods are increasingly being applied to problems in statistical physics, because they unveil aspects that would generally be neglected by traditional approaches. Here we apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to study the passage from the elastic to plastic flow regime in amorphous materials. Sets of particle displacements are obtained from simulations of a 2D amorphous model system in steady shear flow at different shear rates in the athermal limit. PCA produces a low-dimensional representation of the data, in which the principal directions clearly identify distinct differences between elastic (i.e. reversible) and plastic deformation. When deformation is accumulated over larger strains, shear localizes along bands, and PCA provides a quantitative measure of the increased degree of anisotropy in the flow patterns. We suggest that PCA can be a useful analysis technique that complements a traditional statistical description via correlation functions.