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

  • Authors

    • Tintumol Sunny Department of Mathematics, Christ College (Autonomous) Irinjalakuda, Kerala, India
    • Sreena V Department of Mathematics, Christ College (Autonomous) Irinjalakuda, Kerala, India
    • Jaimy Sarah Jacob Department of Mathematics, Baselius College, Kottayam, Kerala, India
    • Preetha Mathew Department of Mathematics, Baselius College, Kottayam, Kerala, India
    • Sunila V PG & Research Department of Statistics, Nehru Arts and Science College, Kanhangad, Kerala, India
    • jobin jose Marian College Kuttikkanam Autonomous, Kerala, India
    https://doi.org/10.14419/nb420z19

    Received date: June 10, 2025

    Accepted date: September 12, 2025

    Published date: September 24, 2025

  • Biblioshiny; Citespace; Neural Differential Equations; Scientometric Analysis; Vosviewer

  • Abstract

    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.

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  • How to Cite

    Sunny, T., V, S., Jacob, J. S. ., Mathew, P. ., V, S. ., & jose, jobin. (2025). A Scientometric Review of Neural Differential Equations: Mapping Research Impact and Collaborative Networks. International Journal of Basic and Applied Sciences, 14(5), 824-833. https://doi.org/10.14419/nb420z19