Particle Swarm Algorithm for Optimizing Hyperparameters and Artificial Neural Network Parameters to Predict Nuclear Binding Energy for Some Odd-Mass Isotopes

Artificial neural networks (ANNs) are essential machine learning models widely used in various fields and applications. These models rely on a vector of parameters, which must be computationally estimated. In this study, a fully connected multilayer perceptron ANN, a modern feedforward neural network with two input layers and two hidden layers (each containing 10 neurons), was developed to estimate the ground state binding energy of isotopes with odd mass numbers ranging from 17 to 339, covering 3414 nuclei. The ANN was applied to three models: the integrated nuclear model, the liquid drop model (LDM), and an empirical formula. The predicted ground state binding energies were evaluated using mean square error (MSE), correlation coefficient (R), and accuracy. To optimize the ANN's performance, parameters such as the number of hidden layers and learning rates were refined using the particle swarm optimization (PSO) algorithm. This optimization reduced the ANN error, achieving an MSE of 0.0099706 and a high accuracy of 99.736% for the LDM model. The correlation coefficient R demonstrated a strong association between the target and output values, confirming the accuracy and robustness of the models. The PSO algorithm's optimization further minimized errors and improved the results, validating the differences in binding energy between the three models and the ANN. This approach underscores the effectiveness of ANNs in modeling complex physical phenomena with high precision.