We don’t have to solve the equations in this (hypothetical) system, just store the values that will define the wave evolution after the probability function will be sampled. None of that time-dependent or time-independent analysis needs to be done!

And, although these values have both time & space parts and are expressed as matrices, they are still just a mean in a complex & possibly curved space. One “simple” example of this is that, instead of PCA, principle component analysis, one can perform PGA, principle geodesic analysis, to account for curved space & time.