how to obtain equations where constants are optimized for different categories in the dataset?

[eloise-croo]

Hi,

I use PySR to derive equations for ship hydrostatics, and my dataset consists of several ship categories (tankers, container vessels...).
I want to obtain equations that have the same form for all ship categories, but where the constants are optimized for each category.
How would you recommend me to proceed?

What I've already tried:

1. obtain equations separately for each ship category, try to find common terms in the pareto front across ship categories, build a custom equation out of that -> only the less complex equations have similar forms across ship types. It isn't obvious to pick common terms.
2. obtain an equation that is fitted simultaneously on all the vessels, and then optimize the constants for each category -> it might be a satisfactory way to go, but I wonder if there are better ways.

I'm curious to read which logic would you use in this case?

Eloïse

[MilesCranmer]

You can use template expressions for this! See the example here: https://ai.damtp.cam.ac.uk/pysr/v1.5.9/examples#parametric-expressions

[eloise-croo]

Awesome! I've now successfully tested it on my data :)
I just want to report that there is a small error in the example code. It should be:
X_with_category = np.column_stack([X, category_p_one])
Thanks!

[MilesCranmer]

Thx!
(@MilesCranmerBot could you please fix this (and backport the fix) in the docs)

[eloise-croo]

I have to ask one more question about model import from pkl. I have no problem importing models that don't use template expressions, but I get an error when using a template expression.

I've tried both:
model = PySRRegressor.from_file(run_directory=model_path)
and
model = PySRRegressor.from_file(run_directory=model_path, expression_spec=template)

and I get the error:
[...] in PySRRegressor.from_file(cls, equation_file, run_directory, binary_operators, unary_operators, n_features_in, feature_names_in, selection_mask, nout, **pysr_kwargs)
1137 assert n_features_in is None
1138 with open(pkl_filename, "rb") as f:
-> 1139 model = cast("PySRRegressor", pkl.load(f))
1141 # Update any parameters if necessary, such as
1142 # extra_sympy_mappings:
1143 model.set_params(**pysr_kwargs)
Exception: error deserializing this value

The pkl file exists.
What I am missing?

[MilesCranmer]

Template expression unfortunately don't support pkl import very well. This is something that is theoretically possible (it has to do with the fact that a function is getting embedded in the file or something) but I haven't yet had the time to fix it. I think part of the fixes are in though (now the function name is based on the hash of the string, for example).