Random Satisfiability Logic-Driven Approach in the Hopfield Neural Networks with Application to COVID-19 Datasets

• Published in: International journal of applied and computational mathematics Vol. 11; no. 3
• Main Author: Abubakar, Hamza
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2025; Springer Nature B.V
• Subjects: Accuracy; Applications of Mathematics; Classification; Complexity; Computational Science and Engineering; COVID-19; Datasets; Entropy; Error reduction; Health surveillance; Logic; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Neural networks; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Rank tests; Statistical analysis; Statistical tests; Support vector machines; Surveillance; Theoretical; Logic Mining; Hopfield Neural Network; Satisfiability; Boolean Logic Integration; COVID-19 Surveillance Data Set
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01941-7

This study proposes a logic-driven satisfiability approach integrated with Hopfield Neural Networks (HNNs) for classifying the COVID-19 Surveillance Data Set (CSDS). The HNN-RAN k SAT model combines Boolean logic-based satisfiability with the Lyapunov energy function of HNNs to extract logical relationships and identify critical features for COVID-19 dataset classification. Evaluated against Logistic Regression (LR), Random Forest (RF), and Support Vector Machine (SVM), the model’s performance was assessed using Accuracy, Hamming Loss, Cross-Entropy Loss, CPU Time, and Bayesian Information Criterion (BIC). HNN-RAN k SAT achieves the highest accuracy of 95.0% at sample size = 500, outperforming RF with 95.0%, SVM with 94.0%, and LR with 93.0% accuracy. It also exhibits the lowest Hamming Loss of 0.04 and Cross-Entropy Loss of 0.16, demonstrating superior classification performance and probabilistic calibration. The model’s logical constraints refine the search space, reducing misclassification errors and improving confidence estimation. However, this comes at the cost of higher computational complexity, with CPU Time increasing to 60 s at 1000 sample size, compared to LR with 20 s, RF with 40 s, and SVM with 50 s. The BIC values for HNN-RAN k SAT at 170 sample size is 1000 reflect its greater model complexity, justified by its robustness in structured problem domains. Statistical tests, including McNemar’s test and Wilcoxon Rank test, confirm the model’s significant improvements (p-values < 0.05), with a large Cohen’s d effect size of 1.21. The hybrid architecture, integrating logic-based reasoning with neural network learning, enables HNN-RANkSAT to handle noisy, incomplete, and high-dimensional data effectively, making it ideal for medical classification tasks. While Random Forest offers a balanced alternative for large-scale problems, HNN-RAN k SAT excels in high-precision tasks like pandemic surveillance.