AlpineGP is a Python library that helps to build algorithms that can identify symbolic models of physical systems starting from data. It performs symbolic regression using a strongly-typed genetic programming approach implemented in the DEAP library. As a natural language for expressing physical models, it leverages the discrete calculus framework 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.

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

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 are a function obtained by parsing the individual tree and possibly other parameters (datasets to compare the individual with). It returns both an error metric between the prediction and the data and the prediction itself.

def eval_MSE_sol(individual: Callable, D: Dataset):

    # ...
    return MSE, prediction

2. Define the functions that return the prediction and the fitness associated to an individual. These functions must have the same arguments. The first argument is always the Callable that represents the individual tree. The functions must be decorated with ray.remote to support distributed evaluation (multiprocessing).

@ray.remote
def predict(individual: Callable, indlen: int, D: Dataset, penalty: float) -> float:

    _, pred = eval_MSE_sol(individual, D)

    return pred

@ray.remote
def fitness(individual: Callable, length: int, D: Dataset, penalty: float) -> Tuple[float, ]:

    MSE, _ = eval_MSE_sol(individual, D)

    # add penalty on length of the tree to promote simpler solutions
    fitness = MSE + penalty*length

    # return value MUST be a tuple
    return fitness,

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,
                               feature_extractors=[len],
                               print_log=True, 
                               config_file_data=config_file_data)

# define training Dataset object (to be used for model fitting)
train_data = Dataset("D", X_train, y_train)

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

# recover the solution associated to the best individual among all the populations
u_best = gpsr.predict(train_data)

# plot the solution
# ...
# ...

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

@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}
}