Asian Journal of Pure and Applied Mathematics

Geological and ecological systems exhibit complex, nonlinear, and dynamic behaviour driven by interactions among physical, biological, and anthropogenic factors. Understanding these systems is critical for sustainable resource management, disaster risk mitigation, and biodiversity conservation. Mathematical modelling provides a quantitative framework to capture system dynamics, identify underlying mechanisms, and predict future behaviour under varying conditions. Machine learning (ML) offers complementary tools to process large-scale, heterogeneous datasets, detect patterns, and improve predictive accuracy. This paper aims to explores the integration of mathematical modelling and machine learning for the analysis of geological and ecological system dynamics. The combined approach enables the development of hybrid models that leverage the interpretability of differential equations, agent-based models, and network analysis with the flexibility and scalability of machine learning algorithms. Applications include landslide and flood risk prediction, species population dynamics, habitat connectivity modelling, and ecosystem service assessment. By combining domain knowledge with data-driven insights, these approaches enhance decision-making for environmental management, policy formulation, and sustainable development. Case studies demonstrate the effectiveness of hybrid models in capturing nonlinear interactions, predicting extreme events, and optimising intervention strategies. The results indicate that integrating mathematical and machine learning models provides a robust framework for understanding and managing complex geological and ecological systems, offering both theoretical insight and practical applicability in diverse environmental contexts.