This thesis develops novel machine-learning approaches for two distinct engineering challenges. First, it implements a machine learning-enhanced systems engineering approach to optimize carbon emissions in electricity markets, using New York State as a case study. The research reveals significant correlations between market mechanisms and environmental outcomes through neural network modeling and interpretive structural analysis, demonstrating how pricing structures can reduce carbon emissions while maintaining market efficiency. Second, it introduces a Kolmogorov-Arnold Network (KAN) model for predicting ruthenium's mechanical and thermodynamic properties in high-entropy superalloys, achieving predictions within 6% of experimental data and outperforming traditional neural networks in both accuracy and efficiency. The model successfully captures phase transitions and melting points through molecular dynamics simulations. These studies showcase the versatility of machine learning in system engineering applications across different scales.