Table 6 Optimal hyperparameters of machine learning models.

From: A comparative machine and deep learning approach for predicting ultimate bearing capacity of shallow foundations in cohesionless soil

ML/DL Model

Optimal hyperparameters

XGBoost

n_estimators = 1172, learning_rate = 0.19767316614730276

LightGBM

n_estimators = 1482, learning_rate = 0.6992380456312691

GBM

n_estimators = 1087, learning_rate = 0.28980775639493667

RF

n_estimators = 108, max_depth = 15, min_samples_split = 2, min_samples_leaf = 1, bootstrap = False

CATBoost

iterations = 1000, learning_rate = 0.1, depth = 6, verbose = 0

AdaBoost

n_estimators = 241, learning_rate = 0.09257405215270152, loss = ‘square’, max_depth = 10, min_samples_split = 4, min_samples_leaf = 1

KNN

n_neighbors = 5, weights = ‘distance’, p = 1, algorithm = ‘auto’

BR

n_estimators = 97, max_samples = 0.9996785133314219, max_features = 0.8255801182352335, bootstrap = False, bootstrap_features = False, max_depth = 12, min_samples_split = 2, min_samples_leaf = 1

DT

max_depth = 8, min_samples_split = 2, min_samples_leaf = 1, max_features = None, splitter = best, criterion = absolute_error

SVM

kernel = rbf, C = 75.62164653446044, epsilon = 0.025523589047330056, degree = 3

ANN

hidden_layer_sizes = 10, activation = logistic, max_iter = 100,000, solver = lbfgs, random_state = 42

DNN

n_layers = 3, units_0 = 113, units_1 = 169, units_2 = 254, learning_rate = 0.002089738484827969, dropout_rate = 0.003010226821045029

CNN

n_conv_layers = 2, filters_0 = 106, filters_1 = 121, kernel_size = 4, learning_rate = 0.003535056792769612, dropout_rate = 0.041472436005474664

RNN

K-Fold MSE Scores: [np.float64(2.265767), np.float64(5.107743), np.float64(4.706106), np.float64(2.874644), np.float64(1.123151)] Mean K-Fold MSE: 3.215483 Best Validation MSE: 1.123151

FFNN

n_layers = 2, units_0 = 43, units_1 = 57, learning_rate = 0.008968117531970703, dropout_rate = 4.784803011470551e-05