Digital Twins in Industrial Applications: Concepts, Mathematical Modeling, and Use Cases

Abstract: Digital Twins (DTs) are virtual representations of physical systems synchronized in real time through Internet of Things (IoT) sensors and computational models. In industrial applications, DTs enable predictive maintenance, fault diagnosis, and process optimization. This paper explores the mathematical foundations of DTs, hybrid modeling techniques, including Physics Informed Neural Networks (PINNs), and their implementation in industrial scenarios. We present key applications, computational tools, and future research directions.