Advanced Scientometric Analysis of Scientific Machine Learning and PINNs: Topic Modeling and Trend Analysis

Scientific machine learning and physics-informed neural networks are novel conceptual approaches that integrate scientific knowledge with methods from data science and deep learning. This emerging field has garnered increasing interest due to its unique features and potential applications. However, key topics and subject-specific applications remain under explored. To address this gap, we conducted a scientometric analysis using large-scale bibliographic and citation data from Scopus. Our study provides a global overview of publication and citation trends, explores the co-occurrence of subject areas to uncover multidisciplinary relationships, and identifies the most collaborative fields. Additionally, we employ a Latent Dirichlet Allocation (LDA) model for topic modeling, introducing a novel information-theoretic approach to determine the optimal number of topics. Furthermore, we conduct a trend analysis based on the convergence behavior of entropy and an interpretation grounded in statistical physics, revealing a consolidation process of research directions indicated as an equilibrium state. Lastly, by analyzing Dirichlet distributions from LDA, we estimate the dimension of the transdisciplinarity of scientific machine learning, offering insights into the primary coherent research areas within this field.