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VOL. 11, ISSUE 2 (2026)
Applications of real and complex analysis with differential equations in statistical modeling for deep learning and scientific computing
Authors
Dr. Muhammed Basheer, Dr. Brinda Halambi, Dr. R Praveena, Gauravi Aditya Lotankar, Dr. B Deepa
Abstract
The advancement of deep learning and
scientific computing has necessitated the integration of rigorous mathematical
frameworks to ensure accuracy, stability, and interpretability. This paper
presents a theoretical exploration of the applications of real analysis,
complex analysis, and differential equations in statistical modeling for deep
learning systems. Real analysis provides the foundation for continuity,
convergence, and optimization, while complex analysis extends these concepts to
higher-dimensional and more flexible representations. Differential equations
contribute to modeling dynamic learning processes and system evolution. The
integration of these mathematical domains enables the development of robust
statistical models that enhance computational efficiency and predictive
performance. This study establishes a unified theoretical framework that
supports advanced modeling techniques in deep learning and scientific
computing, emphasizing mathematical consistency and scalability.
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Pages:28-33
How to cite this article:
Dr. Muhammed Basheer, Dr. Brinda Halambi, Dr. R Praveena, Gauravi Aditya Lotankar, Dr. B Deepa "Applications of real and complex analysis with differential equations in statistical modeling for deep learning and scientific computing". International Journal of Advanced Science and Research, Vol 11, Issue 2, 2026, Pages 28-33
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