Abstract
This study aims to investigate the computation of the partition dimension of various anti-myocardial infarction drugs, a graph-theoretical invariant of molecular graphs representing these drugs, for understanding and computationally characterizing structural properties of molecular networks. To improve the computational modeling of this topological invariant, advanced neural network techniques, specifically graph neural networks (GNNs) and deep neural networks (DNNs), are adopted. The GNN captures topological and molecular connection features from the molecular graph structures, which are then input into the DNN model. The DNN further processes these features to estimate the partition dimension, evaluating training performance, performing regression analysis, and producing error histograms. The model’s predictions are validated against reference values. Moreover, by analyzing the role that symmetry plays in determining the calculation of partition dimension, studying how the GNN takes advantage of permutation invariance concept related to symmetry principles to provide the DNN with symmetry-invariant features, and relating the degree of molecular symmetry to the predictive model’s accuracy and performance, its structural interpretation rather than direct chemical behavior. This dual-model approach permits a comprehensive evaluation of the model’s effectiveness in apprehending the structural characteristics of molecular graphs derived from drug molecules. The results are explicated in detail, focused on prediction accuracy, error distributions, and regression results. Moreover, this graph-theoretical metric analysis of partition dimension supports structure-based drug analysis and computational modeling, rather than direct prediction of pharmacokinetic properties, by integrating artificial neural network applications into pharmaceutical research.