As the main concept, the Digital Twin (DT) shows its potential not only in industry 4.0 but also in other areas. One of the keys that decide the future of DT been known as its model technology. Through models can integrate features, behaviors, and properties of DT artifacts with efficiency, reusability, and interoperability, in order to build a complete mapping between the physical world and digital world, after that realize the ideal DT. This paper aims at comparing and analyzing the DT models in the scientific literature, retracing them from the initial one to the models in most recent researches. Thus, this study also emphasizes several principles of the DT model technology that is related to future work.

Diffusion probabilistic models are powerful generative tools but are purely data-driven, limiting their ability to incorporate domain knowledge—such as physical laws, degradation trends, or engineering priors—in scientific and engineering applications. We introduce Prior-Guided Diffusion Processes (PGDPs), a unified mathematical framework that integrates arbitrary differentiable prior knowledge into the reverse diffusion dynamics by augmenting the score function with a guidance term derived from a prior potential $V(x,t)$ and weighted by a time-dependent strength ${\gamma }_t$. This formulation subsumes existing mechanisms (classifier guidance, model-based diffusion, physics-informed corrections) as special cases. We analyze the guided path measures, providing an upper bound on the Kullback–Leibler divergence between guided and unguided marginals (Theorem 1), quantifying the inherent trade-off between data fidelity and prior satisfaction. Experiments on synthetic data confirm the predicted dependence on ${\gamma }_t$. On the NASA C-MAPSS turbofan benchmark, we enforce compressor-oriented physical constraints (e.g., speed–pressure consistency, monotonicity) within PGDP; remaining useful life scores are reported only as reference metrics under transparent protocols. A cross-domain study on the NASA IGBT accelerated aging dataset, using the same backbone with a replaced physics module, achieves a 99.98% reduction in monotonicity loss, demonstrating generality across distinct degradation mechanisms. PGDP provides a principled, extensible template for knowledge-informed generative modeling with theoretical guarantees and verifiable physical consistency.

Neural architecture search (NAS) is a core technology in AutoML, but it faces challenges such as high computational costs and inefficient evaluation. Traditional NAS methods require fully training each candidate architecture, leading to substantial resource consumption and long evaluation times. This paper introduces a four-stage progressive multi-task learning framework that shifts from brute-force search to performance prediction. By progressively training from simple synthetic data to complex real data, the framework enables efficient architecture performance prediction. The main contributions are a unified progressive predictor paradigm, a deployment-aware multi-task prediction mechanism with dual lightweighting, and a benchmark-aware data-and-transfer framework based on NATS-Bench reconstruction and progressive knowledge distillation. Experiments on 15,000 NATS-Bench architectures with a fixed train–validation–test split (8:1:1) and consistent hyperparameters show a 95.56% correlation-based prediction score, computed as Pearson correlation expressed as a percentage (Pearson correlation 0.9556, R-squared 0.9134), 32-fold training efficiency improvement (37.87 s ± 2.1 s vs. 1247.6 s), and 95.7% convergence stability across five random seeds. Ablation studies, including a Direct Stage-3-Only comparison, quantify component contributions, and benchmarks compare against random forest, XGBoost, and MLP under identical data splits and feature spaces.

Missing-value imputation is critical for industrial monitoring and sensor-to-RUL pipelines in battery and electrical systems. Diffusion models perform well on complex time series, but their necessity for univariate, smooth, small-sample electrical degradation signals remain unclear. We evaluated DDI-E (a conditional diffusion imputer) against linear interpolation (LI) and K-nearest neighbors (KNN) on NASA battery capacity and NASA IGBT leakage-current datasets under 10–90% random missingness, with leave-one-out cross-validation on the battery data. LI/KNN achieved practically sufficient accuracy (battery MAE: 0.007–0.020 Ah), whereas DDI-E did not improve performance (battery MAE: 0.39–0.43 Ah, about 20–58× LI; IGBT MAPE: LI/KNN near 0% vs. DDI-E about 18%). These results indicate an applicability boundary: for univariate, smooth, small-sample electrical degradation data, traditional interpolation is often sufficient, while the extra complexity of diffusion modeling may not yield additional benefit. Combined with our previous positive results on complex multi-channel data, we provide a data-characteristic-driven framework for imputation-method selection and practical guidance for industrial sensor-to-RUL workflows.

Fault diagnosis for complex industrial equipment plays a crucial role in safeguarding production safety and advancing the capabilities of intelligent operation and maintenance. Current deep learning approaches have demonstrated promising accuracy in fault classification tasks; however, their signal representations alone cannot provide a transparent interface for embedded large language models. To tackle the aforementioned challenges, we propose PGA-LLM, a novel fault diagnosis framework for industrial equipment that leverages large language models via probability-guided alignment. First, a variational autoencoder (VAE)-based signal encoder embedded with reconstruction constraints is established. Joint reconstruction and classification objectives balance discriminative representation learning and signal reconstruction. Second, the probability-guided alignment (PGA) module combines fault-class probability guidance with a residual feature path; a learned gate fuses both paths before continuous soft-prompt projection. Furthermore, a progressive three-stage training scheme is adopted, encompassing encoder pre-training, interface optimization, and low-rank adaptation (LoRA) of Qwen2.5-1.5B. Extensive experiments are carried out on four standard datasets, CWRU, Gear, Mixed, and MBHM, and the Stage 2 signal-side output achieves classification accuracies of 97.1%, 99.0%, 93.4%, and 96.3%, respectively. The report-generation branch provides a schema-constrained signal-to-language interface for maintenance-oriented reporting.