## 2 Materials and Methods
### Basic Methods of Generative AI-Driven DTs
Combined with generative AI, transformers improve fault simulation and synthetic data generation, while RL optimizes maintenance strategies by continuously adapting fault diagnosis models based on real-time feedback from DTs [47]. RL enables AI-based DTs to optimize predictive maintenance by continuously learning from real-time equipment data and adapting maintenance strategies based on Industry 4.0/5.0 fault diagnostics results. RL agents interact with digital twins to simulate different maintenance actions, receiving rewards based on reduced downtime, increased fault detection accuracy, and minimized operating costs. Unlike traditional rule-based approaches, RL-based digital twins dynamically refine fault diagnostics and maintenance strategies, improving decision-making as more operational data are processed over time. By combining RL with generative AI, digital twins can simulate rare fault conditions, enabling the RL model to learn from different failure scenarios and make more accurate predictive maintenance recommendations. In complex manufacturing environments, multi-agent RL enables multiple AI-powered digital twins to collaborate, optimizing fault diagnosis and predictive maintenance strategies for interconnected industrial assets [48]. Federated learning enables multiple industrial plants to jointly train predictive maintenance models while maintaining data privacy, and generative AI enhances this process by generating synthetic fault data to increase model robustness in Industry 4.0/5.0. Instead of sharing raw sensor data, federated learning enables AI-based digital twins to exchange model updates, keeping sensitive operational data secure while leveraging collective intelligence across manufacturing plants. Generative models such as GANs and VAEs generate realistic fault scenarios to enrich federated learning models, compensating for imbalanced data sets where certain failure conditions may be underrepresented. AI-based digital twins within a federated learning network continuously update fault diagnostic models using locally generated synthetic data, enabling real-time adaptation to unique operating conditions in different industrial environments. By integrating federated learning with generative AI, industrial systems develop more accurate, context-aware predictive maintenance strategies that reduce downtime and improve fault detection without compromising data security or requiring centralized data storage [49]. The generation of extended data to improve error detection in images or time series signals has been proposed in [50; 51]. Numerical comparisons of different generative AI methods in AI-based DTs for fault diagnosis and predictive maintenance reveal distinct advantages based on accuracy, efficiency, and computational cost. GANs typically improve fault classification accuracy by 5-15% by generating realistic failure data for training models. VAEs achieve anomaly detection precision of 85-95% on average, depending on system complexity and available data. Transformer-based models such as BERT time series variations outperform traditional recursive models by 10-20% in predictive accuracy due to their ability to capture long-range dependencies. Reinforcement learning (RL) approaches reduce maintenance costs by 20-40% by optimizing predictive scheduling strategies compared to rule-based systems. Physics-based generative models reduce false positive rates by 30-50% because they combine physical simulations with AI-based analyses to provide more reliable fault diagnosis. Federated learning with Generative AI improves model generalization across multiple industrial sites while maintaining accuracy at 95%+, although it may require 20-30% more computational resources due to decentralized processing. These comparisons highlight the trade-offs between accuracy, computational cost, and scalability, which is the basis for selecting the right Generative AI techniques for different industrial applications [52; 53].