Models

Regression model

class models.RegressionModels.RegressionModels(H_REFINEMENTS: int = 0)

Bases: object

Base class for regression models.

POD(R_velocity=None, R_pressure=None, scaled=True, testdata=False) → Tuple[ndarray, ndarray]

Perform Proper Orthogonal Decomposition (POD) on the velocity and pressure fields.

If R_velocity or R_pressure is None, the elbow point is used.

Parameters:

R_velocity (int, optional) – Number of modes for the velocity field, by default None
R_pressure (int, optional) – Number of modes for the pressure field, by default None
scaled (bool, optional) – Use scaled data, by default True
testdata (bool, optional) – Use test data, by default True

Returns:

Reduced matrices for the velocity and pressure fields

Return type:

(np.ndarray, np.ndarray)

calculate_error_samples(metric, predict_velocity: ndarray, predict_pressure: ndarray) → Tuple[ndarray, ndarray]

Calculates the error per sample using the specified metric.

Parameters:

metric (Predefined function) – Metric to calculate the error
predict_velocity (np.ndarray) – Predicted velocity data
predict_pressure (np.ndarray) – Predicted pressure data

Returns:

Error per sample for the velocity and pressure fields

Return type:

Tuple[np.ndarray, np.ndarray]

elbow_point(scaled=True) → Tuple[int, int]

Returns the elbow point for the singular values of the velocity and pressure fields.

Parameters:: scaled (bool, optional) – Use scaled data, by default True
Returns:: Elbow point for the velocity and pressure fields
Return type:: (int, int)

inverse_scale_(data_velocity: ndarray, data_pressure: ndarray) → Tuple[ndarray, ndarray]

Inverse scales the data using the trained scalers.

Parameters:

data_velocity (np.ndarray) – Velocity data
data_pressure (np.ndarray) – Pressure data

Returns:

Inverse scaled velocity and pressure data

Return type:

Tuple[np.ndarray, np.ndarray]

load_model(model_velocity_file='RegressionModel_velocity.pkl', model_pressure_file='RegressionModel_pressure.pkl') → Tuple

Loads the trained models from the specified files.

Parameters:

model_velocity_file (str, optional) – File name for the velocity model, by default ‘RegressionModel_velocity.pkl’
model_pressure_file (str, optional) – File name for the pressure model, by default ‘RegressionModel_pressure.pkl’

Returns:

Trained models for the velocity and pressure fields

Return type:

Tuple

mae_test(model_velocity, model_pressure, axis='full'): Calculates the Mean Absolute Error (MAE) for the test data.

mape_test(model_velocity, model_pressure, axis='full'): Calculates the Mean Absolute Percentage Error (MAPE) for the test data.

max_error_test(model_velocity, model_pressure, axis='full'): Calculates the Maximum Error for the test data.

predict_test(model_velocity, model_pressure, rescale=True) → Tuple[ndarray, ndarray]

Predicts the velocity and pressure fields for the test data.

Parameters:

model_velocity (Trained model for the velocity field)
model_pressure (Trained model for the pressure field)
rescale (bool, optional) – Rescale the data, by default True

Returns:

Predicted velocity and pressure fields

Return type:

Tuple[np.ndarray, np.ndarray]

relative_norm(model_velocity, model_pressure, ord=2): Calculates the relative norm for the test data.

rmse_test(model_velocity, model_pressure, axis='full'): Calculates the Root Mean Squared Error (RMSE) for the test data.

save_model(model_velocity, model_pressure, model_velocity_file='RegressionModel_velocity.pkl', model_pressure_file='RegressionModel_pressure.pkl')

Saves the trained models to the specified files.

Parameters:

model_velocity (Trained model for the velocity field)
model_pressure (Trained model for the pressure field)
model_velocity_file (str, optional) – File name for the velocity model, by default ‘RegressionModel_velocity.pkl’
model_pressure_file (str, optional) – File name for the pressure model, by default ‘RegressionModel_pressure.pkl’

scale_(data_velocity: ndarray, data_pressure: ndarray) → Tuple[ndarray, ndarray]

Scales the data using the trained scalers.

Parameters:

data_velocity (np.ndarray) – Velocity data
data_pressure (np.ndarray) – Pressure data

Returns:

Scaled velocity and pressure data

Return type:

Tuple[np.ndarray, np.ndarray]

singular_values(scaled=True) → Tuple[ndarray, ndarray]

Returns the singular values for the velocity and pressure fields.

Parameters:: scaled (bool, optional) – Use scaled data, by default True
Returns:: Singular values for the velocity and pressure fields
Return type:: (np.ndarray, np.ndarray)

class models.LinearRegression.LinearRegressionModel(H_REFINEMENTS: int = 0)

Bases: RegressionModels

Trains a Linear Regression model for the velocity and pressure fields.

train(X_r_velocity: ndarray, X_r_pressure: ndarray)

Trains the Linear Regression model for the velocity and pressure fields (each).

Parameters:

X_r_velocity (np.ndarray) – Velocity data
X_r_pressure (np.ndarray) – Pressure data

Returns:

Trained models for the velocity and pressure fields

Return type:

(LinearRegression, LinearRegression)

class models.GaussianProcessRegressor.GaussianProcessRegressionModel(H_REFINEMENTS: int = 0)

Bases: RegressionModels

Trains a Gaussian Process Regression model for the velocity and pressure fields.

load_model(model_velocity_file='GaussianRegressionModel_velocity.pkl', model_pressure_file='GaussianRegressionModel_pressure.pkl'): Loads the trained models from the specified files.

save_model(model_velocity, model_pressure, model_velocity_file='GaussianRegressionModel_velocity.pkl', model_pressure_file='GaussianRegressionModel_pressure.pkl'): Saves the trained models to the specified files.

train(X_r_velocity: ndarray, X_r_pressure: ndarray, kernel=DotProduct(sigma_0=1) + WhiteKernel(noise_level=1))

Trains the Gaussian Process Regression model for the velocity and pressure fields (each).

Parameters:

X_r_velocity (np.ndarray) – Velocity data
X_r_pressure (np.ndarray) – Pressure data
kernel (sklearn.guassian_process.kernels, optional) – Kernel for the Gaussian Process Regression model, by default DotProduct() + WhiteKernel()

Returns:

Trained models for the velocity and pressure fields

Return type:

(GaussianProcessRegressor, GaussianProcessRegressor)

class models.RBFInterpolator.RadialBasisRegressionModel(H_REFINEMENTS: int = 0)

Bases: RegressionModels

Trains a Radial Basis Function Interpolator model for the velocity and pressure fields.

load_model(model_velocity_file='radialBasisModel_velocity.pkl', model_pressure_file='radialBasisModel_pressure.pkl'): Loads the trained models from the specified files.

predict_test(model_velocity, model_pressure, rescale=True)

Predicts the velocity and pressure fields for the test data.

Parameters:

model_velocity (RBFInterpolator) – Trained model for the velocity field
model_pressure (RBFInterpolator) – Trained model for the pressure field
rescale (bool, optional) – Rescale the data, by default True

Returns:

Predicted velocity and pressure fields

Return type:

(np.ndarray, np.ndarray)

save_model(model_velocity, model_pressure, model_velocity_file='LinearRegressionModel_velocity.pkl', model_pressure_file='LinearRegressionModel_pressure.pkl'): Saves the trained models to the specified files.

train(X_r_velocity: ndarray, X_r_pressure: ndarray, kernel: str = 'multiquadric', epsilon: float = 1)

Trains the Radial Basis Function Interpolator model for the velocity and pressure fields (each).

Parameters:

X_r_velocity (np.ndarray) – Velocity data
X_r_pressure (np.ndarray) – Pressure data
kernel (str, optional) – Kernel for the RBFInterpolator model, by default ‘multiquadric’
epsilon (float, optional) – Epsilon for the RBFInterpolator model, by default 1

Returns:

Trained models for the velocity and pressure fields

Return type:

(RBFInterpolator, RBFInterpolator)

class models.ANN.ANN(H_REFINEMENTS: int = 0)

Bases: RegressionModels

Class for training an Artificial Neural Network (ANN) model for the velocity and pressure fields.

train(X_r_velocity: ~numpy.ndarray, X_r_pressure: ~numpy.ndarray, epochs: int = 10000, batch_size: int = 32, plot_learning: bool = True) -> (<class 'keras.src.models.sequential.Sequential'>, <class 'keras.src.models.sequential.Sequential'>)

Trains the ANN model for the velocity and pressure fields.

Builds the models and trains them (preferably on a GPU). Separate models are built for the velocity and pressure fields.

Parameters:

X_r_velocity (np.ndarray) – Velocity data
X_r_pressure (np.ndarray) – Pressure data
epochs (int, optional) – Number of epochs, by default 10_000
batch_size (int, optional) – Batch size, by default 32
plot_learning (bool, optional) – Plot the learning curves, by default True

Returns:

Trained models for the velocity and pressure fields

Return type:

(tf.keras.models.Sequential, tf.keras.models.Sequential)

class models.ANN.ANNHyperModel(param_matrix_train, X_r)

Bases: HyperModel

Class for defining the hyperparameters of the ANN model.

build(hp)

Builds a model.

Parameters:: hp – A HyperParameters instance.
Returns:: A model instance.