AlpineGP

AlpineGP is a Python library that solves symbolic regression problems using Genetic Programming. It provides a high-level interface to the DEAP library and leverages the high-performance distributed computing functionalities provided by the ray library.

Beside solving classical symbolic regression problems involving algebraic equations (see, for example, the benchmark problems contained in the SRBench repository), AlpineGP is specifically design to help identifying interpretable, symbolic models of physical systems starting from data. To this aim, it exploits as a natural and effective language to express physical models (i.e., conservation laws) a discrete calculus framework, including tools from discrete differential geometry and discrete exterior calculus, defined and implemented in the library dctkit.

AlpineGP has been introduced in the paper Discovering interpretable physical models with symbolic regression and discrete exterior calculus, along with several benchmark problems.

Installation

Dependencies should be installed within a conda environment. We recommend using mamba since it is much faster than conda at solving the environment and downloading the dependencies. To create a suitable environment based on the provided .yaml file, use the command

$ mamba env create -f environment.yaml

Otherwise, update an existing environment using the same .yaml file.

After activating the environment, clone the git repository and launch the following command

$ pip install -e .

to install a development version of the library.

Running the tests:

$ tox

Generating the docs:

$ tox -e docs

Usage

Setting up a symbolic regression problem in AlpineGP involves several key steps:

1. Define the function that computes the prediction associated to an individual (model expression tree). Its arguments may be a function obtained by parsing the individual tree and possibly other parameters, such as the dataset needed to evaluate the model. It returns both an error metric between the prediction and the data and the prediction itself.

def eval_MSE_sol(individual, dataset):

    # ...
    return MSE, prediction

1. Define the functions that return the prediction and the fitness associated to an individual. These functions must have the same arguments. In particular:
   • the first argument is always the batch of trees to be evaluated by the current worker;
   • the second argument must be the toolbox object used to compile the individual trees into callable functions;
   • the third argument must be the dataset needed for the evaluation of the individuals. Both functions must be decorated with ray.remote to support distributed evaluation (multiprocessing).

@ray.remote
def predict(trees, toolbox, data):

    callables = compile_individuals(toolbox, trees)

    preds = [None]*len(trees)

    for i, ind in enumerate(callables):
        _, preds[i] = eval_MSE_sol(ind, data)

    return preds

@ray.remote
def fitness(trees, toolbox, true_data):
    callables = compile_individuals(toolbox, trees)

    fitnesses = [None]*len(trees)

    for i, ind in enumerate(callables):
        MSE, _ = eval_MSE_sol(ind, data)
        
        # each fitness MUST be a tuple (required by DEAP)
        fitnesses[i] = (MSE,)

    return fitnesses

3. Set and solve the symbolic regression problem.

# read parameters from YAML file
with open("ex1.yaml") as config_file:
    config_file_data = yaml.safe_load(config_file)

# ...
# ...

# load datasets...

# define the primitive set (input/output types)
pset = gp.PrimitiveSetTyped(...)

# rename arguments of the tree function
pset.renameArguments(ARG0="u")

# define extra common arguments of fitness and predict functions
common_params = {'penalty': penalty}

# create the Symbolic Regression Problem object
gpsr = gps.GPSymbolicRegressor(pset=pset, fitness=fitness.remote,
                               predict_func=predict.remote, common_data=common_params,
                               print_log=True, 
                               config_file_data=config_file_data)

# wrap tensors corresponding to train and test data into Dataset objects (to be passed to
# fit and predict methods)
train_data = Dataset("D", X_train, y_train)
test_data = Dataset("D", X_test, y_test)

# solve the symbolic regression problem
gpsr.fit(train_data)

# compute the prediction on the test dataset given by the best model found during the SR
pred_test = gpsr.predict(test_data)

A complete example notebook can be found in the examples directory.

Citing

@article{Manti_2024,
    doi = {10.1088/2632-2153/ad1af2},
    url = {https://dx.doi.org/10.1088/2632-2153/ad1af2},
    year = {2024},
    publisher = {IOP Publishing},
    volume = {5},
    number = {1},
    pages = {015005},
    author = {Simone Manti and Alessandro Lucantonio},
    title = {Discovering interpretable physical models using symbolic regression and discrete exterior calculus},
    journal = {Machine Learning: Science and Technology}
}