The recent advancements in the research area have primarily focused on integrating machine learning techniques with physical systems to enhance predictive capabilities and model complex dynamics. A notable trend is the use of neural networks, particularly in the form of neural operators and differential neural networks, to address challenges in system parameter identification, hidden physics discovery, and real-time fault diagnosis. These approaches leverage the strengths of machine learning, such as handling sparse and noisy data, while maintaining physical consistency through physics-informed constraints. Another significant development is the application of reduced-order modeling and surrogate modeling frameworks, which combine data-driven methods with traditional physical modeling to achieve efficient and accurate predictions in areas such as electric machine design and uncertainty quantification. The integration of Fourier transforms and Gaussian processes in these frameworks has shown superior performance in preserving physical information and reducing computational costs. Additionally, the use of self-organizing neural networks for thermal image-based fault diagnosis demonstrates a streamlined approach that is well-suited for edge device deployment. Overall, the field is moving towards more integrated and efficient solutions that bridge the gap between data-driven methods and traditional physical modeling, enabling better performance and broader applicability in various domains.