Shaping new limits: the future evolution of mathematical models and control strategies

Chafaa  Hamrouni

doi:10.59400/adecp2859

Shaping new limits: the future evolution of mathematical models and control strategies

Chafaa Hamrouni Department of Computer Sciences, Kurma University College, Taif University, Kurma 2935, Kingdom of Saudi Arabia

Article ID: 2859

Keywords: artificial intelligence; computational learning algorithms; hierarchical modeling; chaotic flow dynamics; geometric fractals; nanoscale engineering; regulatory mechanisms in dynamic systems

Abstract

Mathematics underpins scientific advancement and fuels innovation across disciplines. In the next decade, the convergence of differential equations and control theory with emerging technologies, especially artificial intelligence and machine learning will redefine modeling, prediction, and decision-making for complex systems. This integration enhances predictive fidelity, reveals latent structure in high-dimensional data, and accelerates discovery cycles. Recent work in environmental forecasting illustrates these gains, where deep learning has achieved high-accuracy prediction of atmospheric variables and pollutant concentrations. Multi-scale modeling will be central to linking phenomena across spatial and temporal ranges, enabling impactful applications from nanotechnology to fluid dynamics. Parallel progress in fractal geometry offers new tools to analyze, quantify, and optimize intricate structures and dynamics, informing studies of urban growth, heterogeneous media, and chaotic flows. AI-assisted control strategies are poised to transform healthcare, autonomous systems, and communication networks by delivering adaptive, data-driven policies that improve robustness, efficiency, and safety. This review synthesizes the state of the art at the intersection of differential equations, control processes, and AI, surveying methodological advances, benchmark applications, and emerging computational pipelines. It also identifies open challenges including model interpretability, data scarcity across scales, stability guarantees for learning-based controllers, and reproducible evaluation protocols that demand tightly coordinated, interdisciplinary research. By unifying mathematical rigor with AI-driven inference and control, the field is positioned to build more predictive, reliable, and efficient solutions for the next generation of scientific and engineering problems.

Published

2025-09-30

How to Cite

Hamrouni, C. (2025). Shaping new limits: the future evolution of mathematical models and control strategies. Advances in Differential Equations and Control Processes, 32(3). https://doi.org/10.59400/adecp2859

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Issue

Vol. 32 No. 3 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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