The dataset used in this study comprised 532 structurally diverse compounds with experimentally reported analgesic activity values collected from published literature sources. Each compound was numerically characterized by 227 molecular descriptors computed using cheminformatics tools. These descriptors covered multiple categories, including constitutional, topological, geometrical, electronic, and physicochemical properties.

The target variable in this work represents the analgesic activity score expressed on a continuous scale. For classification purposes, a binary activity label (active or inactive) was assigned using a statistically derived threshold value of the continuous variable. Prior to modeling, the dataset was normalized using min–max scaling to ensure that all input features contributed equally during network training.

To prevent overfitting and improve computational efficiency, a stepwise feature elimination approach was employed. This technique iteratively removes low-importance descriptors while monitoring model performance at each step, ensuring that only the most informative features correlated with analgesic activity are retained.

The selection criterion combined the Pearson correlation coefficient (R) and relative prediction error (ERAM%), which allowed the identification of descriptors contributing most significantly to the prediction accuracy.

Performance was assessed using two statistical indicators: the correlation coefficient (R) and the average absolute relative error (ERAM).

The correlation coefficient (R) quantifies the linear relationship between predicted ( y c a l ) and experimental ( y exp ) values, as given by Equation 1: R = ∑ i = 1 N y exp − y ¯ exp y c a l − y ¯ c a l ∑ i = 1 N y exp − y ¯ exp 2 ∑ i = 1 N y c a l − y ¯ c a l 2 (1)

The average absolute relative error (ERAM) evaluates the average percentage deviation of predicted values from the experimental ones, as expressed in Equation 2: E R A M = 100 n ∑ i = 1 n y exp − y c a l y exp (2)

Here y exp represents the experimental value, y c a l the predicted value, y ¯ exp and y ¯ c a l their respective means, and n the number of observations.

The Artificial Neural Network (ANN) was implemented and trained in MATLAB® using a feed-forward multilayer perceptron architecture. The model design followed a systematic optimization strategy involving iterative adjustment of architectural and training parameters.

The ANN model was implemented with:

Input layer: optimized reduced descriptor set

Hyperparameter tuning was carried out through a combination of grid search and performance-based evaluation. The number of hidden neurons, learning rate, and regularization factors were optimized to minimize the average absolute relative error (ERAM%) between predicted and experimental outputs.

The overall modeling process is summarized in Figure 1, which presents the flowchart of the ANN optimization procedure. The workflow begins with descriptor calculation and preprocessing, followed by feature selection, network initialization, and iterative optimization of model parameters. Each iteration involved evaluating model performance on a validation subset to ensure stability and reproducibility.

This structured approach ensures that the final ANN model is both predictively accurate and computationally efficient, providing a reproducible framework for modeling analgesic activity in structurally diverse molecular datasets.

The impact of descriptor reduction on model performance was systematically evaluated to determine the optimal set of molecular features influencing analgesic activity prediction. As illustrated in Figure 2, progressive elimination of descriptors with minimal correlation to biological response resulted in a steady improvement in the mean absolute relative error (ERAM%) until reaching a subset of 105 descriptors, beyond which predictive performance began to decline.

This indicates that the retained descriptors capture the most informative structural and physicochemical characteristics relevant to analgesic bioactivity. These include parameters describing molecular connectivity, polarity, and hydrogen-bonding potential—factors known to modulate receptor binding affinity and pharmacodynamic behavior [6, 7].

The observed behavior aligns with previous QSAR and deep learning studies reporting that redundant or weakly correlated features introduce noise and reduce model generalization [8]. Feature reduction not only improved accuracy but also enhanced computational efficiency, mitigating overfitting, one of the key challenges in high, dimensional neural modeling [9, 10].

Following descriptor optimization, a series of ANN architectures were systematically evaluated to identify the configuration offering the best balance between predictive accuracy and complexity. The Levenberg–Marquardt (LM) algorithm was selected for training due to its rapid convergence and robustness in nonlinear parameter optimization.

The final optimized topology (Table 1), consisted of three hidden layers, each employing a tansig activation function, followed by a single linear output neuron. This configuration achieved a correlation coefficient of R = 0.959 and an ERAM of 0.433%, demonstrating a nearly perfect alignment between predicted and experimental analgesic activity values.

Regression plots (Figure 3) show near-linear correlations for both training and validation datasets, confirming excellent generalization without bias toward specific chemical subgroups. The LM-based training achieved convergence within fewer than 50 iterations, outperforming conventional gradient-descent approaches in both speed and stability [11].

Comparable studies have generally reported lower accuracies when employing shallow or single-hidden-layer ANNs for QSAR prediction, with correlation coefficients (R) typically ranging between 0.85 and 0.93 [12]. The superior performance achieved in the present work can be attributed to the joint optimization of both the network architecture and the feature selection process, which significantly improved the model’s capacity to capture complex nonlinear structure–activity relationships [13, 14]. Table 2 presents a comparative summary between our findings and previously published studies, highlighting key aspects such as dataset size (number of compounds), model type and topology, descriptor or feature set employed, and the corresponding reported performance metrics.

This study successfully developed and optimized an Artificial Neural Network (ANN) framework for the accurate prediction of analgesic activity, achieving excellent regression (R = 0.959) and classification (accuracy = 98.01%) performance metrics. By integrating a rigorous descriptor reduction strategy with systematic ANN topology optimization, the proposed model effectively balanced predictive accuracy, interpretability, and computational efficiency. The resulting framework outperformed traditional QSAR and machine learning methods highlighting the superiority of deep ANN architectures in capturing nonlinear structure–activity relationships.

The inclusion of 105 carefully selected molecular descriptors enhanced both model transparency and robustness, establishing direct links between topological, electronic, and physicochemical features and their biological relevance. This balance between interpretability and performance underscores the growing potential of AI-assisted modeling to accelerate rational drug discovery and virtual screening in pharmacology.

Beyond methodological advances, this work contributes to the broader objectives of green and sustainable drug development by reducing experimental dependence and resource consumption. Future perspectives include extending the optimized ANN framework to other pharmacological classes, implementing transfer learning for multitarget predictions, and integrating explainable AI tools to further elucidate mechanistic insights.

Overall, the proposed hybrid feature selection–ANN modeling strategy represents a reliable, interpretable, and eco-efficient approach to predictive pharmacology, paving the way for more intelligent, data-driven discovery of next-generation analgesics.