This review provides a comprehensive overview of recent advancements in computational methods for modeling, simulation, and optimization of complex systems in materials engineering, mechanical engineering, and energy systems. It highlights the integration of artificial intelligence (AI) with traditional computational methods, emphasizing key trends and applications. The paper discusses various advanced computational algorithms, including AI methods, and introduces novel strategies for materials production and optimization in energy systems. It demonstrates significant improvements in accuracy and efficiency, offering valuable insights for researchers and practitioners. The review synthesizes state-of-the-art developments and suggests directions for future research, underscoring the critical role of these methods in advancing engineering and technological solutions. The review covers a wide range of topics, including advanced computational methods for system analysis and prediction, such as mathematical modeling, numerical simulation, machine learning, and optimization techniques. It also explores the application of AI in various fields, including materials science, engineering, and energy systems. The paper presents several case studies, such as the use of the sparrow search algorithm for network traffic prediction, the hybrid-flash butterfly optimization algorithm for engineering optimization, and the attention-based isolation forest for anomaly detection. Additionally, it discusses the application of AI in geothermal heat flow prediction, support vector methods for mechanical materials, and the modeling of chaotic behavior. The review also addresses the development of composite materials, functionally graded materials, and fluoro perovskites, highlighting the role of advanced computational methods in predicting their properties and structures. It emphasizes the importance of elastic constants in describing mechanical properties and the application of AI in predicting fiber properties. The paper concludes by discussing the potential of AI and computational methods in optimizing, modeling, and predicting complex systems, and their significance in advancing materials technology and engineering solutions.This review provides a comprehensive overview of recent advancements in computational methods for modeling, simulation, and optimization of complex systems in materials engineering, mechanical engineering, and energy systems. It highlights the integration of artificial intelligence (AI) with traditional computational methods, emphasizing key trends and applications. The paper discusses various advanced computational algorithms, including AI methods, and introduces novel strategies for materials production and optimization in energy systems. It demonstrates significant improvements in accuracy and efficiency, offering valuable insights for researchers and practitioners. The review synthesizes state-of-the-art developments and suggests directions for future research, underscoring the critical role of these methods in advancing engineering and technological solutions. The review covers a wide range of topics, including advanced computational methods for system analysis and prediction, such as mathematical modeling, numerical simulation, machine learning, and optimization techniques. It also explores the application of AI in various fields, including materials science, engineering, and energy systems. The paper presents several case studies, such as the use of the sparrow search algorithm for network traffic prediction, the hybrid-flash butterfly optimization algorithm for engineering optimization, and the attention-based isolation forest for anomaly detection. Additionally, it discusses the application of AI in geothermal heat flow prediction, support vector methods for mechanical materials, and the modeling of chaotic behavior. The review also addresses the development of composite materials, functionally graded materials, and fluoro perovskites, highlighting the role of advanced computational methods in predicting their properties and structures. It emphasizes the importance of elastic constants in describing mechanical properties and the application of AI in predicting fiber properties. The paper concludes by discussing the potential of AI and computational methods in optimizing, modeling, and predicting complex systems, and their significance in advancing materials technology and engineering solutions.