Mathematical Modelling of Dynamic Systems for Forecasting using Big Data and Machine Learning

Dynamic systems are fundamental in describing and analyzing time-evolving processes across diverse domains including energy management, transportation networks, and economic systems. Accurate forecasting of such systems is critical for effective decision-making, strategic planning, and resource optimization. The exponential growth of Big Data technologies has enabled the collection of large-scale, high-dimensional datasets from various sources, while machine learning algorithms have demonstrated remarkable capabilities in pattern recognition and predictive modeling. This study presents an innovative mathematical modelling framework that synergistically integrates Big Data analytics with machine learning techniques for enhanced dynamic system forecasting. The proposed hybrid methodology combines traditional mathematical models based on differential equations and state-space representations with advanced data-driven approaches to capture both structural dynamics and complex nonlinear behaviors. The framework leverages Long Short-Term Memory networks to model temporal dependencies and employs distributed computing platforms for handling massive datasets efficiently. Experimental validation was conducted using real-world electricity demand data from smart grid systems, demonstrating that the hybrid model achieved significant improvements in forecasting accuracy, reducing the Root Mean Squared Error by up to 21% compared to classical mathematical models and by 12% compared to standalone machine learning approaches. The findings underscore the potential of this integrated methodology for real-time forecasting applications and its broad applicability across multiple domains requiring reliable prediction of complex dynamic systems.

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