Postdoctoral Researcher at Santa Cruz State University, Ilhéus, Bahia, Brazil
Dr. Rômulo Damasclin C. Santos 🇧🇷 is an accomplished applied mathematician and fluid dynamics specialist whose career bridges deep theoretical insight with computational precision. With a Ph.D. in Applied Mathematics from the University of Porto 🎓 and postdoctoral research at the prestigious Instituto Tecnológico de Aeronáutica (ITA) 🔬, he seamlessly integrates mathematical rigor with practical modeling. His passion lies in deciphering real-world physical phenomena using tools such as Partial and Integro-Differential Equations, Complex Analysis, and Fluid Dynamics 💨. He has held diverse teaching and research roles across Brazil, including UESC and UEMS, contributing significantly to academic development nationwide 📘. A published innovator, Dr. Santos has developed original computational methods like HODIM and Hybrid Adaptive DRM, alongside expertise in C++, Python, and MATLAB 💻. Actively involved in peer-review and editorial duties, his interdisciplinary approach is anchored in innovation, collaboration, and mathematical excellence. 🧠🌐
Professional Profile
🎓 Education
Dr. Santos’s educational path reflects an unyielding drive for mastery in applied mathematics and engineering. He earned his Ph.D. in Applied Mathematics from the University of Porto (Portugal) in 2018, focusing on fluid dynamics through advanced numerical and analytical models 📘. Prior to that, he completed an M.Sc. in Mechanical Engineering at the Federal University of Itajubá (UNIFEI), specializing in flow machines and thermofluid systems 🌪️. His academic journey began with a Bachelor’s degree in Mathematics at the Federal University of Acre (UFAC), where he concurrently explored fractal geometry and object-oriented programming 🧮💻. Currently, he is further expanding his scientific breadth through postdoctoral research in Physics at ITA, one of Brazil’s foremost institutions in science and technology 🔬. This multifaceted academic background underpins his ability to approach problems from both abstract and applied angles.
👨🏫 Professional Experience
Dr. Santos has amassed a wealth of academic and research experience across Brazil’s most respected institutions 🏛️. He currently serves as a Postdoctoral Research Fellow at UESC and concurrently holds a professorship in Mathematics at UEMS, demonstrating his dual commitment to research and education 📚. His past roles include teaching positions at Federal Institutes (Santa Catarina, Acre), Mato Grosso State University, and UVERSO University Center, often within the engineering or mathematics departments 🧠. Whether substituting or leading research, he brought clarity and innovation to diverse academic environments. With more than a decade of academic engagement, he has nurtured student talent, advanced new methodologies, and contributed to institutional development nationwide. His dynamic roles—spanning from mathematical modeling to engineering theory—reflect a professional identity grounded in flexibility, excellence, and forward-thinking mentorship. 🎓🧪
🔬 Research Interests
Dr. Santos’s research is a fusion of theoretical depth and computational elegance 🧬. His core interests revolve around Fluid Dynamics, Turbulence Modeling, and Heat Transfer, particularly in incompressible Newtonian fluids 🌊. His toolkit includes advanced methods like Immersed Boundary Method (IBM), Smoothed-Particle Hydrodynamics (SPH), and LES, all tailored to simulate real-world chaotic flows. He integrates Partial, Integral, and Integro-Differential Equations to decipher the complex interplay in dynamical systems 🔁. Using programming languages such as C++, Python, and MATLAB, he develops original algorithms, including the High-Order Dynamic Integration Method (HODIM) and Hybrid Adaptive DRM for large-scale systems 🖥️. His mathematical framework draws from Complex Analysis, Functional Analysis, and Numerical Methods, making his contributions valuable across engineering, physics, and applied mathematics domains. His ambition is to model nature’s complexities through computation and logic, offering insights that cross traditional disciplinary boundaries. 🔗🌌
🏅 Awards and Honors
Dr. Santos has earned national and international recognition through prestigious academic engagements and editorial responsibilities 🌍. His Ph.D., validated in Brazil by UFRGS, exemplifies international academic excellence 🎓. As a reviewer and editorial board member for several renowned journals—such as Journal of Applied Fluid Mechanics, Brazilian Journal of Physics, and ASTES Journal—he contributes to the global dissemination of scientific knowledge 📖. Moreover, his commitment to innovation is officially recognized through computer program registrations with INPI, Brazil’s national patent authority 🏷️. He is a respected member of elite professional bodies, including the Brazilian Society for Applied and Computational Mathematics (SBMAC), Brazilian Mathematical Society (SBM), and the International Association of Engineers and Computer Scientists (IAENG) 🤝. These affiliations, coupled with his published innovations, affirm his role as a forward-thinking thought leader in applied mathematics and engineering systems.
📚 Publications Top Note
1. Hypermodular Neural Operators: Ramanujan-Kantorovich Synthesis in Sobolev Approximation Theory
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Authors: Rômulo D. C. dos Santos & Jorge H. de Oliveira Sales
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Year: 2025 (July 8)
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Source: HAL Open Science (Preprint)
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Citation: HAL ID: hal-05115451
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Summary: This work proposes a fusion of Ramanujan summability concepts with Kantorovich-type neural operators to form “hypermodular” neural frameworks. It operates within Sobolev spaces and demonstrates superior convergence and approximation behavior, especially near boundaries. The authors establish convergence results and operator stability using Sobolev norms.
2. Symmetrized Neural Network Operators in Fractional Calculus: Caputo Derivatives, Asymptotic Analysis, and the Voronovskaya–Santos–Sales Theorem
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Authors: Rômulo D. C. dos Santos, Jorge H. de Oliveira Sales, Gislan S. Santos
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Year: 2025 (June 30)
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Source: Axioms (MDPI), Journal Article
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DOI: 10.3390/axioms14070510
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Summary: This article introduces symmetrized neural network operators tailored to fractional calculus and Caputo derivatives. It develops a new asymptotic theorem named after the authors, offering enhanced convergence analysis for fractional neural networks. Applications include fractional signal processing and modeling of dissipative systems.
3. Innovations in Neural Approximation: Uniting Symmetrized Kantorovich-Ramanujan Operators within Sobolev Spaces
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Authors: Rômulo D. C. dos Santos & Jorge H. de Oliveira Sales
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Year: 2025 (June 23)
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Source: HAL Open Science (Preprint)
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Citation: HAL ID: hal-05115451 (version 1)
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Summary: A foundational version of the unified Kantorovich-Ramanujan operator framework for neural networks. This work extends approximation theory in Sobolev spaces using Ramanujan-style summability corrections and operator symmetrization.
4. Advancing Neural Approximation: The Role of Kantorovich-Ramanujan-Santos-Sales Operators in Modern Computation
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Authors: Rômulo D. C. dos Santos & Jorge H. de Oliveira Sales
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Year: 2025 (May 26)
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Source: Zenodo (CERN), Preprint
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DOI: 10.5281/ZENODO.15514812
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Summary: Introduces a new family of operators combining Kantorovich-Ramanujan theory with neural networks, emphasizing boundary regularization, smoothness control, and numerical stability. A Voronovskaya-type expansion is derived for these operators.
5. Stochastic Fractional Neural Operators: A Symmetrized Approach to Modeling Turbulence in Complex Fluid Dynamics
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Authors: Rômulo D. C. dos Santos & Jorge H. de Oliveira Sales
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Year: 2025 (May 21)
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Source: arXiv (Computer Science > Machine Learning)
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DOI: 10.48550/ARXIV.2505.14700
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Summary: This paper explores stochastic extensions of fractional neural operators applied to fluid turbulence. By incorporating symmetrized neural kernels and stochastic perturbations, the authors model uncertainty and chaotic behavior in turbulent flow systems.
6. Anomalous Gradients in AI: Multivariate Fractional Calculus Unifying Landau Inequalities and Deep Operator Stability
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Author: Rômulo D. C. dos Santos
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Year: 2025 (May 18)
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Source: Zenodo (CERN), Preprint
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DOI: 10.5281/ZENODO.15454789
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Summary: Investigates the connection between multivariate fractional calculus and gradient stability in AI. The study proposes a new operator framework addressing anomalous gradients through generalizations of Landau inequalities.
7. Extension of Symmetrized Neural Network Operators with Fractional and Mixed Activation Functions
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Authors: Rômulo D. C. dos Santos & Jorge H. de Oliveira Sales
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Year: 2025 (May 11)
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Source: The Journal of Engineering and Exact Sciences
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DOI: 10.18540/jcecvl11iss1pp21662
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Summary: This work extends neural approximation theory using fractional and mixed-type activation functions (like q-deformed and inverse polynomial activations). It presents a new Jackson-type inequality and convergence analysis.
8. Neural Network Operators for the New Era of Fractional Calculus: Bridging Analysis and Artificial Intelligence Systems
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Author: Rômulo D. C. dos Santos
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Year: 2025 (April 6)
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Source: Zenodo (CERN), Preprint
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DOI: 10.5281/ZENODO.15163347
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Summary: Introduces neural operators that operate natively in the fractional calculus domain. Sets a foundational framework unifying AI learning mechanisms with fractional integral and differential operators.
9. Beyond Traditional Approximation: Advanced Voronovskaya-Damasclin Theory for Neural Network Approximation in Fractional Calculus
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Author: Rômulo D. C. dos Santos
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Year: 2025 (March 30)
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Source: Zenodo (CERN), Preprint
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DOI: 10.5281/ZENODO.15109088
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Summary: Provides theoretical extensions of Voronovskaya’s theorem into the realm of neural approximation using fractional operators. Establishes sharp asymptotic error bounds for fractional neural network functionals.
10. Bifurcations, Stability and Numerical Analysis of Turbulent Flow (Bidimensional)
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Author: Rômulo D. C. dos Santos
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Year: 2025 (April 17)
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Source: Observatório de la Economía Latinoamericana
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DOI: 10.55905/oelv23n4-125
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Summary: Focuses on the use of fractional and numerical methods to model bifurcation behavior in two-dimensional turbulent flows. Combines theory from dynamical systems with neural-based numerical solvers.
🧩 Conclusion
Dr. Rômulo Damasclin C. Santos is a polymath in the truest sense—merging theory, simulation, and real-world application into a cohesive scientific narrative 🔄. His journey from the Amazon to Europe and back to Brazil’s top academic circles reflects determination, intellectual courage, and innovation 🌎. As an educator, he has shaped minds across Brazil; as a researcher, he has expanded the boundaries of what’s possible in fluid dynamics and numerical modeling 💡. His multidisciplinary mindset enables him to tackle complex problems with originality, backed by robust mathematical foundations and computational fluency. In a world increasingly driven by scientific modeling and simulation, Dr. Santos stands out as a pioneering figure ready to lead the charge in engineering mathematics and technological advancement 🚀📊.