Handling physical units in PySR when distilling ML models

[chikchikpanda]

Hi all,

I have a question regarding the interpretation and handling of physical units in PySR, particularly in workflows where PySR is used to distill a trained ML model rather than fit directly to observations.

My current workflow is:

1. Train an XGBoost model using physically meaningful predictors (each with well-defined units).
2. Use the XGBoost predictions as targets for PySR to obtain interpretable symbolic equations.
3. Inputs to both models are typically normalized or standardized.

This works well in terms of accuracy and symbolic compression, but I am unsure how to interpret physical units in the resulting PySR equations.

Specifically:

• In this ML-distillation setting, should PySR-derived equations be interpreted as dimensionless surrogate relationships rather than physically dimensioned laws?
• Does normalization/standardization effectively remove unit consistency, even if the original variables have physical units?
• Are dimensional constraints or unit-aware symbolic regression features in PySR/SymbolicRegression.jl meaningful or recommended in this context?
• Is there any suggested best practice for reporting or post-processing units when physical interpretability is a goal?

I would appreciate any guidance, references, or examples from similar use cases.

[MilesCranmer]

Hi @chikchikpanda,
Have you tried out the dimensional constraints feature? https://ai.damtp.cam.ac.uk/pysr/v1.5.9/examples.html#_10-dimensional-constraints - let me know if this helps.
Cheers,
Miles