Integrating Optimization Strategies with Machine Learning for Improved Artificial Intelligence Performance

Optimization is crucial to the growth of artificial intelligence (AI) and machine learning (ML), enabling effective solutions for complex challenges across various fields. This paper investigates the interplay between optimization techniques and AI/ML approaches, emphasizing the foundational roles of mathematical modeling, partial differential equations, and operator theory. We highlight recent advancements in areas such as inverse problems and variational methods, showcasing how these developments enhance problem-solving efficiency and robustness in modeling. The findings underscore the reciprocal influence of optimization and AI/ML, concluding with potential future research avenues that address existing challenges and explore novel applications in diverse domains.

Optimization, Artificial Intelligence, Machine Learning, Partial Differential Equations

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