Purpose. The objective of this study is to analyze the concept of digital twins as a technology integrating complexity theory and artificial intelligence, and to examine their applications across various fields. Particular emphasis is placed on mathematical approaches to the construction of digital twins, their distinctions from traditional mathematical models, and future development prospects.

Methods. This research employs an interdisciplinary approach, incorporating an analysis of contemporary technologies such as physics-informed neural networks, reduced-order models, graph neural networks, and reservoir computing. A comparison of first-principles and data-driven modeling methods is conducted, with a focus on their integration for creating hybrid digital twins.

Results. The findings demonstrate that digital twins possess unique characteristics, including dynamism, adaptability, and bidirectional interaction with physical objects. The key advantages and limitations of various mathematical approaches are identified, encompassing their applicability in industry, medicine, economics, and other domains. A general mathematical formalization of a digital twin, integrating traditional models and machine learning methods, is proposed.

Conclusion. The prospects for the development of digital twins are outlined, including the creation of end-to-end ecosystems and the advancement of hybrid approaches for modeling complex nonlinear processes. The importance of further integration of complexity theory and artificial intelligence methods to enhance the accuracy and adaptability of virtual models is emphasized. Digital twins present new opportunities for the forecasting and management of complex systems under uncertainty, establishing them as a pivotal tool in science, industry, and society.