Flexibility of Maximum-Stochastic Satisfiability in Stochastic Hopfield Neural Networks with Applications to Materials Engineering Datasets

This study evaluates the flexibility of mapping Maximum Stochastic Satisfiability (MAX-SSAT) onto Stochastic Hopfield Neural Networks (SHNNs) for applications in materials engineering datasets. MAX-SSAT is a critical decision problem in optimization, machine learning, and artificial intelligence, with significant implications for engineering, where accurate decision-making is essential. Although the Hopfield Neural Network (HNN) has gained popularity due to its capacity to address various optimization problems, its ability to effectively model uncertainty remains limited. This research addresses this limitation by utilizing SHNNs, which introduce stochastic elements into the decision-making process, thereby enhancing the representation of uncertainty in complex optimization tasks. The study compares SHNNs and HNNs across multiple performance metrics, including Global Minimum Ratio (Zm), Fitness Energy Landscape (FEL), Error Rate, and KL Divergence and Hamming Loss, cross-entropy loss, and risk prediction accuracy. Empirical results demonstrate the superior performance of SHNNs over HNNs. Specifically, SHNNs achieved an average Zm of 92.5%, outperforming HNNs' 82.3%. Additionally, SHNNs exhibited a higher FEL score of 0.87 compared to HNNs’ 0.73 and faster convergence times, averaging 45 seconds versus 68 seconds for HNNs. In the Material Failure Prediction Dataset, SHNNs achieved a classification accuracy of 91.2%, outperforming HNN with 85.4%, and demonstrated a lower cross-entropy loss of 0.075 compared to HNN with 0.125. Similarly, SHNNs outperformed HNNs in the Concrete Compressive Strength Dataset, achieving 92.1% accuracy compared to HNN with 87.5% accuracy. These findings highlight the flexibility of SHNN for improved performance in materials classification and risk prediction tasks, providing a robust model in representing MAX-SSAT problems in real-world engineering applications. Future research could extend these models to more complex optimization tasks across diverse engineering domains.