Principal component analysis of collective flow in relativistic heavy-ion collisions

Abstract

Abstract In this paper, we implement principal component analysis (PCA) to study the single particle distributions generated from thousands of $$\mathtt {VISH2+1}$$VISH2+1 hydrodynamic simulations with an aim to explore if a machine could directly discover flow from the huge amount of data without explicit instructions from human-beings. We found that the obtained PCA eigenvectors are similar to but not identical with the traditional Fourier bases. Correspondingly, the PCA defined flow harmonics $$v_n^\prime $$vn′ are also similar to the traditional $$v_n$$vn for $$n=2$$n=2 and 3, but largely deviated from the Fourier ones for $$n\ge 4$$n≥4. A further study on the symmetric cumulants and the Pearson coefficients indicates that mode-coupling effects are reduced for these flow harmonics defined by PCA.