Prompting Neural-Guided Equation Discovery Based on Residuals

This code accompanies the paper "Prompting Neural-Guided Equation Discovery Based on Residuals" accepted at Discovery Science 2025.

Residuals for Equation Discovery (RED) is a post-processing method for Equation Discovery that improves a given equation in a targeted manner, based on its residuals

We test the method on five equation discovery systems (EDS) NeSymReS, SymbolicGPT, E2E, PySR and GPLearn.

In total we implemented six methods to postprocess the initial equation suggested by the EDS (RED, Permute, Hyper Parameter Grid, Constant Fitting, CVGP, Seeded GPlearn)

Installation

All packages are specified for Python version 3.10

pip install -r requirements.txt

Experiments

The experiments can be reproduced using the commands specified in experiments.sh.

The scripts src/fit_func_[model].py start the experiments for the respective model. The postprocessing methods are located in src/post_processing_methods.

Add new Equation Discovery Model

We only need a method to load the pretrained model and a method which handels the call of the model.

def load_model():
    model = ...
    fitfunc = partial(call,
                      model=model,
                      args=args
                      )
    return fitfunc


def call(model, X_df, Y_df, args):
    equation = model.fit(X_df.to_numpy(), Y_df.to_numpy())
    equation = str(sympify(equation))
    output = evaluate_equation(args, equation, X_df, Y_df)
    return output

Add a new Operator

New Operator can be added in src/equation_class/math_class.
Afterward, they have to be added in src/syntax_tree/syntax_tree.py in the dictionary self.operator_to_class and in src/equation_classes/infix_to_prefix.py in the method getPriority