  Classification of cluster variables in cluster algebras (in particular,
Grassmannian cluster algebras) is an important problem, which has direct
application to computations of scattering amplitudes in physics. In this paper,
we apply the tableaux method to classify cluster variables in Grassmannian
cluster algebras $\mathbb{C}[Gr(k,n)]$ up to $(k,n)=(3,12), (4,10)$, or
$(4,12)$ up to a certain number of columns of tableaux, using HPC clusters.
These datasets are made available on GitHub. Supervised and unsupervised
machine learning methods are used to analyse this data and identify structures
associated to tableaux corresponding to cluster variables. Conjectures are
raised associated to the enumeration of tableaux at each rank and the tableaux
structure which creates a cluster variable, with the aid of machine learning.
