Let me rephrase the question to see if I understand it correctly:

Why do you go for a single piece of hardware when in fact, you could already do this on several GPGPUs and one CPU or use several CPUs on the cloud.?

It could probably be done using these techniques but the answer resides in the fact that if the computation of the phase transition is done very fast for a particular "measurement matrix" (i.e. a particular "sensor") then we could foresee its use in near-real time in instances where the "measurement matrix" would be time dependent (such as the atmosphere....). This would be important in that it would allow to figure out if these new "sensors" can be actually used (as opposed to being mere lab constructions).