Modelling diameter distribution by deep learning algorithms: A case study in Anatolian Black Pine stands in Ilgın (Konya) region

This study aims to model the diameter distributions of Anatolian Black Pine (Pinus nigra subsp. pallasiana) stands using Deep Learning Algorithms (DLA)'s model, an artificial intelligence technique. Utilizing data from 408 sample plots collected from pure Anatolian Black Pine stands distributed across Ilgın, Akşehir, and Aşağıçiğil Forest Planning Units within Ilgın Forest Enterprise Directorate from the Konya Regional Directorate, the parameters of 3-parameter Weibull and 4-parameter Johnson SB probability density functions were calculated by using the maximum likelihood method, the moment and percentile methods based on various percentile and moment values of diameter distributions and hybrid methods. Deep Learning Algorithm (DLA) models were trained with a fixed hyperbolic tangent sigmoid activation function and 100 neurons, incorporating four different hidden layer configurations (3, 5, 7, and 10 hidden layers), along with the customization of three hyperparameters (learning rate, momentum rate, and early stopping) that can be considered as solutions to the overfitting problem. When evaluating the performance of Deep Learning Algorithm models in diameter distributions, the best predictive 3-parameter Weibull probability density function (calculated with 31% and 63% percentile values) yielded a Mean Absolute Error (MAE) of 41.701 stems/ha, Root Mean Square Error (RMSE) of 57.486 stems/ha, RMSE% of 55.481%, R² value of 0.701, AIC value of 9590, and BIC value of 11226. In contrast, the most successful Deep Learning Algorithm model—featuring 7 hidden layers with a momentum rate hyperparameter of 0.001—produced an RMSE of 49.193 stems/ha, RMSE% of 47.628%, R² value of 0.784, AIC value of 1905, and BIC value of 2239. In this regard, it can be concluded that the Deep Learning model provides more accurate results in modeling diameter distributions compared to traditional probability density functions.