Fitting a feedback loop to data points
This is probably an awful approach to fitting points and prediction.

There's no reason to expect that a PRNG will do a good job at fitting points.  Interpolation is effective because we think that not all curves are equally likely.  Some kind of Occam's razor applies: all else being equal, the "simpler" the curve, the more likely that it is as a plausible model.

Thus, linear regression is useful precisely because not all curve shapes are possible; only straight lines.  Empirically, straight lines occur more often than crazy-wiggly shapes.  Similarly, polynomial regression is useful because a low-order polynomial is more likely than a high-order polynomial.

Now consider the following approach: try to fit the data you already have to an arbitrary function (with no restrictions on the function or the shape of the curve; all functions are valid/legal models).  Well, that'll be an absolutely terrible approach at prediction.  You'll be able to find a function that exactly fits all of the data you already have, but (most likely) it will be absolutely useless at predicting values you haven't seen -- it'll be absolutely useless at generalization / prediction.  Essentially, you'll have massively overfitted the data set.

Now a PRNG is designed to behave like a true-random generator.  In other words, all sequences of outputs are supposed to be equally likely (or, at least, you can't tell the difference).  Fitting your data to a true-random generator will be useless at prediction/generalization.  For the same reason, fitting your data to a PRNG is likely to be useless at prediction/generalization.

You should probably read about the "no free lunch" theorems for machine learning and prediction: https://en.wikipedia.org/wiki/No_free_lunch_theorem, http://www.aihorizon.com/essays/generalai/no_free_lunch_machine_learning.htm, http://no-free-lunch.org/.  To be effective at prediction, the learning technique must embed some bias about what hypotheses/models are more likely.  A true-random generator has no bias and thus is useless.  A PRNG behaves like a true-random generator and thus will probably be useless (or, to the extent it has bias, its bias is towards distributions that are very unlikely to appear in nature).