Assume that the spatiotemporal behaviour of a system $z(t,x,y)$ is given by a model $M(n,m)$. We know that this system can be in different phase i.e. $z$ can exhibit qualitatively different macroscopic properties for different $m,n$ - but we can't delineate the boundaries analytically.
Now, assume we are given a large number of simulation outputs over a range of $m$ and $n$ values. Our task is to classify the simulation outputs in phases.
My question is, how would one approach this problem generally? Statistical tests? Clustering? Addressing this question would be a very pedagogical example of how to identify a phase quantitatively.