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Welcome to use SGML!

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1 Introduction

Solution-guided machine learning (SGML) is a universal approach designed to enhance the extrapolation capabilities of AI models, as detailed in the paper [Thin-Walled Struct. 200 (2024) 111984]. To simplify the integration of this method into diverse projects, we have encapsulated it within a user-friendly Python package. By leveraging the functions provided in the package, users can effortlessly apply the SGML method to enhance the extrapolation capabilities of their AI models.

The current version of the package incorporates various regression models, including implementations for Artificial Neural Network, Support Vector Regression, AdaBoost Regression, Bayesian Ridge Regression, and Ridge Regression models. It's worth noting that we are actively working to expand the package's capabilities, and future releases will introduce additional models to further enhance its universality and applicability to a broader range of AI projects.

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2 Preparation

• The functionality of this package depends on the following external libraries:

        <img src="https://img.shields.io/badge/pandas-2.x.x-orange" alt="pandas" />      <img src="https://img.shields.io/badge/NumPy-1.x.x-orange" alt="NumPy" />      <img src="https://img.shields.io/badge/Matplotlib-3.x-orange" alt="Matplotlib" />      <img src="https://img.shields.io/badge/joblib-Any-blue" alt="joblib" />      <img src="https://img.shields.io/badge/tqdm-Any-blue" alt="tqdm" />      <img src="https://img.shields.io/badge/PyTorch-2.x.x-orange" alt="PyTorch" />      <img src="https://img.shields.io/badge/scikit_learn-1.3-orange" alt="scikit_learn" />

• You can easily install SGML by using the installation package in the attachment or by running the following command:

  pip install SGML

• The required project data is in .csv format, displayed in the table below, with the column index encompassing the features and labels necessary for machine learning.

  | ID | x1 | x2 | ... | y | |---|---|---|---|---| | 1 | ... | ... | ... | ... | | 2 | ... | ... | ... | ... | | ... | ... | ... | ... | ... |

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3 API

[!IMPORTANT]

• The solution function will be returned with the data type of a function for the given solution. Users can assign it a name for subsequent guidance in machine learning.

• When the parameters are set to 'default' or left unspecified, the default values for those parameters will be applied.

• Once you have defined your chosen model, remember to utilize additional modules for training and further analysis.

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3.1 Solution Function

def SGML.create_solution_function(

expression = str,

variables = list

)

return function

[!TIP] expression : Solution expression, such as 'a**3+2*b+1'.

variables : List of variables included in the solution, such as ['a', 'b'].

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3.2 Artificial Neural Network-based Model

class SGML.ann(

train_path = str,

test_path = str,

feature_names = list,

lable_names = list,

solution_functions = list,

model_loadpath = str,

model_savepath = str,

hidden_layers = list,

activation_function = object,

batch_size = int,

criterion = object,

optimizer = object,

learning_rate = float,

epochs = int

)

[!TIP] train_path : The file path for loading the training set.

test_path : The file path for loading the testing set.

feature_names : List containing feature names, such as ['x1', 'x2', ...].

lable_names : List containing label names, such as ['y'].

solution_functions : List containing solution function names, such as [solution1, solution2, ...]. default=None

model_loadpath : The file path for the existing model. default=None

model_savepath : Path to save the model. default=None

hidden_layers : The hidden layer architecture, denoted as [4, 8, 2], signifies the presence of three hidden layers with node counts of 4, 8, and 2, respectively. default=[8, 8]

activation_function : The activation function--refer to PyTorch Documentation for details. default=torch.nn.PReLU()

batch_size : The number of training samples used by the model during each parameter update. default=Total number of samples

criterion : The loss function--refer to PyTorch Documentation for details. default=torch.nn.MSELoss()

optimizer : The optimizer--refer to PyTorch Documentation for details. default=torch.optim.Adam()

learning_rate : default=0.01

epochs : default=5000

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3.3 Support Vector Regression-based Model

class SGML.svr(

train_path = str,

test_path = str,

feature_names = list,

lable_names = list,

solution_functions = list,

model_loadpath = str,

model_savepath = str,

kernel = str,

degree = int,

gamma = str or float,

coef0 = float,

tol = float,

C = float,

epsilon = float,

shrinking = bool,

cache_size = float,

verbose = bool,

max_iter = int

)

[!TIP] The API reference for the parameters train_path, test_path, feature_names, lable_names, solution_functions, model_loadpath, and model_savepath can be found in Section 3.2.

kernel : Refer to sklearn.svm.SVR for detailed information, and the same applies to the following parameters. default='linear'

degree : default=3

gamma : default='scale'

coef0 : default=0.0

tol : default=1e-3

C : default=1.0

epsilon : default=0.1

shrinking : default=True

cache_size : default=200

verbose : default=False

max_iter : default=-1

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3.4 AdaBoost Regressor-based Model

class SGML.adaboost(

train_path = str,

test_path = str,

feature_names = list,

lable_names = list,

solution_functions = list,

model_loadpath = str,

model_savepath = str,

estimator = object,

n_estimators = int,

learning_rate = float,

loss = str,

random_state = int

)

[!TIP] The API reference for the parameters train_path, test_path, feature_names, lable_names, solution_functions, model_loadpath, and model_savepath can be found in Section 3.2.

estimator : Refer to sklearn.ensemble.AdaBoostRegressor for detailed information, and the same applies to the following parameters. default=LinearRegression()

n_estimators : default=50

learning_rate : default=1.0

loss : default='linear'

random_state : default=None

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3.5 BayesianRidge Regressor-based Model

class SGML.bayesianridge(

train_path = str,

test_path = str,

feature_names = list,

lable_names = list,

solution_functions = list,

model_loadpath = str,

model_savepath = str,

max_iter = int,

tol = float,

alpha_1 = float,

alpha_2 = float,

lambda_1 = float,

lambda_2 = float,

alpha_init = float,

lambda_init = float,

compute_score = bool,

fit_intercept = bool,

copy_X = bool,

verbose = bool

)

[!TIP] The API reference for the parameters train_path, test_path, feature_names, lable_names, solution_functions, model_loadpath, and model_savepath can be found in Section 3.2.

max_iter : Refer to sklearn.linear_model.BayesianRidge for detailed information, and the same applies to the following parameters. default=None

tol : default=1e-3

alpha_1 : default=1e-6

alpha_2 : default=1e-6

lambda_1 : default=1e-6

lambda_2 : default=1e-6

alpha_init : default=None

lambda_init : default=None

compute_score : default=False

fit_intercept : default=True

copy_X : default=True

verbose : default=False

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3.6 Ridge Regressor-based Model

class SGML.ridge(

train_path = str,

test_path = str,

feature_names = list,

lable_names = list,

solution_functions = list,

model_loadpath = str,

model_savepath = str,

alpha = float,

fit_intercept = bool,

copy_X = str or bool,

max_iter = int,

tol = float,

solver = str,

positive = bool,

random_state = int

)

[!TIP] The API reference for the parameters train_path, test_path, feature_names, lable_names, solution_functions, model_loadpath, and model_savepath can be found in Section 3.2.

alpha : Refer to [sklearn.line