## 2 Materials and Methods
### Basic Methods of Generative AI-Driven DTs  
GenAI-driven DTs leverage advanced ML techniques (such as GANs and VAEs) to simulate and generate realistic data scenarios. These models learn patterns from IIoT data, allowing them to predict, optimize, and replicate complex behaviors of real-world systems. Reinforcement learning (RL) further enables DTs to adapt to dynamic environments by testing and refining decision-making strategies. Natural language processing (NLP) techniques allow these DTs to interpret and integrate textual data such as maintenance logs, operator reports, and technical documentation into their analyses. Additionally, transfer learning helps leverage pre-trained models to accelerate the development and deployment of AI-driven generative DTs in various industrial contexts [44]. GANs enhance AI-based DTs by generating synthetic sensor data that replicates real-world failure conditions, helping predictive maintenance models detect rare and complex failure modes in Industry 4.0/5.0 environments. GANs create different failure scenarios by learning statistical patterns of normal and faulty operating states, enabling digital twins to improve fault diagnostic accuracy even when historical failure data are limited. The generator synthesizes realistic fault signals, while the discriminator improves its ability to distinguish between real and artificial faults, strengthening the fault detection and anomaly recognition capabilities of the digital twin. By continuously learning from live sensor data, GAN-based digital twins detect deviations from normal operation in real time, enabling early failure prediction and reducing unplanned downtime. When combined with reinforcement learning, GANs optimize maintenance decisions based on synthetic fault simulations, while federated learning ensures secure model training across multiple industrial sites without sharing sensitive operational data [45]. VAEs enhance AI-based DTs by learning the underlying distribution of normal operating data, enabling the detection of deviations that signal potential failures in predictive maintenance for Industry 4.0/5.0. VAEs encode high-dimensional sensor data into a lower-dimensional latent space, capturing salient features of machine behavior and facilitating the identification of anomalies that indicate emerging failures. VAEs reconstruct sensor signals from compressed latent representations, and when the reconstruction error exceeds a threshold, it suggests the presence of an unknown or abnormal fault condition. Unlike traditional deterministic models, VAEs generate probabilistic results, enabling digital twins to assess the uncertainty of failure predictions and reduce false positives in predictive maintenance. VAE can be combined with RL to optimize maintenance decisions based on detected anomalies, while federated learning enables secure, decentralized model training across multiple industrial facilities without the need to share raw sensor data [46]. Transformers, such as Bidirectional Encoder Representations from Transformers (BERT), improve predictive maintenance by processing sensor data in large time series, capturing complex relationships in industrial systems, and improving fault diagnostics in Industry 4.0/5.0. Transformers' self-driving mechanism enables AI-based digital twins to analyze long-term relationships in sensor data, identifying subtle fault patterns that traditional machine learning models may miss. Transformer models pre-trained on extensive industrial data sets can be tuned to specific device types, enabling more accurate fault detection and predictive maintenance tailored to unique operating conditions. Transformers analyze streaming data in real time, learning about normal machine behavior and flagging anomalies that indicate early signs of failure, reducing unplanned downtime in manufacturing and industrial processes.