Artificial Intelligence in Mathematical Modeling of Complex Systems: A Comprehensive Review of Concepts, Applications, and Future Directions

This paper investigates how to include artificial intelligence (AI) methods into complex system mathematical modelling. Traditionally, techniques like system dynamics, network theory, and algebraic modelling are used to study complex systems, which are distinguished by dynamic interactions, nonlinear behaviour, and high dimensionality. The emergence of artificial intelligence (AI), namely machine learning (ML) and deep learning (DL), has created new possibilities for improving forecast accuracy, revealing latent patterns, and allowing adaptive behaviour in these systems. Because AI algorithms are so good at learning from massive amounts of data, they may be used for time series forecasting, anomaly detection, optimisation, and decision-making. In fields like image and speech recognition, bioinformatics, and autonomous systems, neural network models—which are essential to machine learning and deep learning—have shown an amazing capacity to represent and analyse complicated phenomena. Additionally, the integration of data-driven modelling with conventional theoretical frameworks improves the capacity to capture system behaviours that are challenging to represent analytically. Complex system optimisation and self-regulation are further supported by AI-enabled adaptive control systems. In conclusion, combining AI and mathematical modelling enhances simulation accuracy while offering a revolutionary toolkit for comprehending and controlling complex systems in the fields of science, industry, and society.