A Scientometric Review of Neural Differential Equations: Mapping Research Impact and Collaborative Networks

Neural Differential Equations (NDEs) represent an emerging class of machine learning models that combine the strengths of neural networks and differential equations to model continuous-time dynamics with high interpretability. This study presents a comprehensive bibliometric analysis of NDE research using data extracted from the Scopus database. Analytical tools such as Biblioshiny, VOSviewer, and ‎CiteSpace were employed to uncover patterns, trends, and structural relationships within the field. The annual scientific production shows a ‎significant growth trajectory, with a peak in 2023, indicating rising scholarly interest. Most relevant authors include Rackauckas, Nopens, ‎and Chien, whose contributions have shaped the theoretical and applied dimensions of NDEs. Co-citation networks of both authors and ‎journals revealed well-defined research clusters focused on deep learning techniques, scientific machine learning, and graph-based modeling. ‎Country-wise analysis highlights the dominance of the United States and China, followed by notable contributions from the UK, Canada, ‎and India. Keyword co-occurrence and trend analysis identified emerging themes such as “transformer,” “graph neural networks,” and “scientific machine learning,” reflecting ongoing methodological innovation. Thematic evolution and mapping show a shift from foundational ‎terms to more specialized and interdisciplinary applications. Identified research gaps suggest a need for stronger theoretical integration, ‎benchmark development, and application in real-world domains, offering practical implications for researchers and practitioners in AI, engineering, and applied sciences‎.