From Equations to Algorithms: A Bibliometric Analysis and Visualization of Physics-Informed Machine Learning Research

Physics-Informed Machine Learning (PIML) is a highly promising hybrid model, with a combination of physical principles and machine learning methods, to improve predictive performance, interpretability, and computationally efficiency in the simulation of complex real-world systems. PIML enhances the trustworthiness of forecasting by incorporating physics-based restrictions into data-driven models, retaining causal consistency. This bibliometric work was done via Biblioshiny, VOSviewer and CiteSpace on the publications indexed on the Scopus database and gives a complete picture of the intellectual and structural development of the field. The analysis will demonstrate that the number of scientific publications is growing rapidly each year, with the most prominent authors, journals, and sources of publications. Co-citation networks are used to discover significant thematic clusters, whereas the analysis of international collaboration reveals the key contribution of China and the United States to the field development. The thematic shift of the foundational issues of machine learning and neural networks to the new fields of digital twins, parameter estimation, and anomaly detection is evidenced by keyword co-occurrence and citation burst analysis. Regardless of the rapid growth, uncertainty quantification, real-time data integration, and interdisciplinary standardization have research gaps. Overall, the findings provide a current overview of the evolving PIML research landscape and highlight emerging directions for future investigation.