ADVANCED MACHINE LEARNING ALGORITHMS FOR PREDICTIVE MODELLING IN COMPLEX SYSTEMS: INTEGRATING MATHEMATICAL OPTIMIZATION AND STATISTICAL METHODS FOR ENHANCED DECISION-MAKING

Abstract

Predictive modelling in complex systems remains a difficult task, largely because such systems exhibit nonlinear interactions, uncertain or evolving dynamics, and often rely on incomplete measurements. These challenges are compounded by the practical need to make decisions that remain reliable even when the underlying information is uncertain. In response to this, the present study introduces an integrated framework that brings together machine learning methods, mathematical optimization, and statistical inference with the aim of improving predictive accuracy, uncertainty characterization, and decision support.

The approach involves a structured pipeline that includes data preparation, feature construction, and the use of both ensemble-based models and deeper learning architectures. Hyperparameters are tuned using Bayesian strategies and evolutionary search techniques, while uncertainty estimates are produced through calibrated ensemble methods and Bayesian-inspired procedures. To illustrate how the framework performs in practice, a synthetic time series representing a complex system is used, accompanied by detailed diagnostic checks and evaluations that reflect decision-making considerations.

The results indicate that the proposed framework yields noticeably lower prediction errors than standard reference models and produces uncertainty intervals that align more closely with observed variability. In decision-focused tests, the method also leads to better outcomes when costs or risks associated with incorrect predictions are taken into account. Incorporating multi-objective optimization further exposes the balance between predictive accuracy and computational demands, offering guidance for selecting models in real-world applications.

Taken together, the findings suggest that combining machine learning with optimization and statistical reasoning can provide more trustworthy, interpretable, and practically useful predictions for complex systems.