Prof. Dr. Murat Sarı was invited as a speaker at the "Matematik ve Yapay Zeka Zirvesi" (Mathematics and AI Summit), which was held at Erzurum Technical University in Erzurum, Turkey. This presentation discusses how data-driven and AI-based models can be used to complement classical mathematical modelling for complex real-world systems. Focusing on concepts rather than technical details, it highlights opportunities, limitations and open questions in using machine learning for prediction, control and decision support in physical, biological and socio-economic applications.

This presentation focuses on the role of artificial intelligence in data-driven modelling of complex systems. Without concentrating on a single case study, it shows how learning algorithms can be combined with classical mathematical models to describe real behaviours more efficiently. The discussion begins with a brief review of traditional modelling workflows based on physical laws, numerical solvers and parameter estimation, and explains why these approaches can become prohibitively expensive or impractical when systems are high-dimensional, strongly nonlinear or only partially observed. Against this background, AI-based surrogates and reduced models that learn from experimental or simulated data are introduced. Rather than presenting detailed formulas, the emphasis is placed on general principles: how to design meaningful input–output representations, how to respect physical constraints and how to avoid overfitting when data are limited. Illustrative examples include applications ranging from environmental processes to biomedical and socio-economic systems, always at a conceptual level. Throughout, AI tools are presented as part of a broader modelling toolbox, not a replacement for theory and experiments. The presentation has highlighted future directions such as hybrid physics–AI approaches, uncertainty quantification and the responsible use of data-driven models in real decision-making contexts.