Finding generalized form of equation from multiple traces?

[AlbanMor]

Hi!
First off, congratulation on this awesome package!

I was wondering if there is a way to use PySR to identify a generalized form of the equation ruling different traces. A simple example would be identifying the equation "ax+b" from the following traces : y1 = 2x1+3, y2= 3x2+5, y3= -1x3 + 4 etc.

Thank you in advance!

[MilesCranmer]

Hi @AlbanMor,
Thanks for the kind words.

Very interesting idea. Right now there is not a built-in way to do this. But ideas appreciated.

Right now you could hack it – I think the easiest way to do something like this is to simply turn it into a single equation search (rather than 3), and pass the index of the equation (y1, y2, y3) as an additional feature. Then it could find something like this:

y = (2 > i) * 2 * x1 + (3 > i) * (i > 1) * 3 * x2 - (i > 2) * x3 + 2 + i

which as you can see gives you all y1 (i=1), y2 (i=2), and y3 (i=3) in a single expression. Furthermore it will try to find the minimal equation that fits all three at once.

(You can pass greater as one of the operators)

I'm sure there's a smarter way to do this though... Ideas appreciated!

Cheers,
Miles

[AlbanMor]

Thank you so much for the quick reply.
I'll give that a try but could you explain to me how that would diverge from solving separately for the three traces?

[AlbanMor]

I don't know the intricacies of your code but what I understand is that you first "evolve the operator tree" (sorry if i don't use the right terms) and then fit the constants values to the data. if these are separate steps, the fitting procedure could be done separately on each traces and return an average goodness of fit for that "operator tree". You could then judge how successful the "new evolved tree" is and continue to the next "evolution/mutation". That would ensure that the same "operator tree" is used for all traces.