This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of residual loss, thereby indicating the complexity of different sections within the entire domain. By analyzing residual loss pointwise and aggregating it over specific intervals, we identify critical regions requiring focused attention. This strategic segmentation allows for the application of tailored neural networks in identified subdomains, each characterized by varying levels of complexity. Additionally, the proposed method trains and saves the model progressively based on performance metrics, thereby conserving computational resources in sections where satisfactory results are achieved during the training process. The effectiveness of PDD is demonstrated through its application to complex PDEs, where it significantly enhances accuracy and conserves computational power by strategically simplifying the computational tasks into manageable segments.

Lung nodule classification is crucial for the diagnosis and treatment of lung diseases. However, selecting appropriate metrics to evaluate classifier performance is challenging, due to the prevalence of negative samples over positive ones, resulting in imbalanced datasets. This imbalance often necessitates the augmentation of positive samples to train powerful models effectively. Furthermore, specific medical tasks require tailored augmentation methods, the effectiveness of which merits further exploration based on task objectives. This study conducted a detailed analysis of commonly used metrics in lung nodule detection, examining their characteristics and selecting suitable metrics based on this analysis and our experimental findings. The selected metrics were then applied to assessing different combinations of image augmentation techniques for nodule classification. Ultimately, the most effective metric was identified, leading to the determination of the most advantageous augmentation method combinations.

Reliability and robustness are fundamental requisites for the successful integration of deep-learning models into real-world applications. Deployed models must exhibit an awareness of their limitations, necessitating the ability to discern out-of-distribution (OOD) data and prompt human intervention, a critical competency. While several frameworks for OOD detection have been introduced and achieved remarkable results, most state-of-the-art (SOTA) models rely on supervised learning with annotated data for their training. However, acquiring labeled data can be a demanding, time-consuming or, in some cases, an infeasible task. Consequently, unsupervised learning has gained substantial traction and has made noteworthy advancements. It empowers models to undergo training solely on unlabeled data while still achieving comparable or even superior performance compared to supervised alternatives. Among the array of unsupervised methods, contrastive learning has asserted its effectiveness in feature extraction for a variety of downstream tasks. Conversely, auto-encoders are extensively employed to acquire indispensable representations that faithfully reconstruct input data. In this study, we introduce a novel approach that amalgamates contrastive learning with auto-encoders for OOD detection using unlabeled data. Contrastive learning diligently tightens the grouping of in-distribution data while meticulously segregating OOD data, and the auto-encoder augments the feature space with increased refinement. Within this framework, data undergo implicit classification into in-distribution and OOD categories with a notable degree of precision. Our experimental findings manifest that this method surpasses most of the existing detectors reliant on unlabeled data or even labeled data. By incorporating an auto-encoder into an unsupervised learning framework and training it on the CIFAR-100 dataset, our model enhances the detection rate of unsupervised learning methods by an average of $5.8\%$. Moreover, it outperforms the supervised-based OOD detector by an average margin of $11\%$.

Logistics operations demand real-time visibility and rapid response, yet minute-level traffic speed forecasting remains challenging due to heterogeneous data sources and frequent distribution shifts. This paper proposes a Deep Operator Network (DeepONet)-based framework that treats traffic prediction as learning a mapping from historical states and boundary conditions to future speed states, enabling robust forecasting under changing scenarios. We project logistics demand onto a road network to generate diverse congestion scenarios and employ a branch–trunk architecture to decouple historical dynamics from exogenous contexts. Experiments on both a controlled simulation dataset and the real-world Metropolitan Los Angeles (METR-LA) benchmark demonstrate that the proposed method outperforms classical regression and deep learning baselines in cross-scenario generalization. Specifically, the operator learning approach effectively adapts to unseen boundary conditions without retraining, establishing a promising direction for resilient and adaptive logistics forecasting.

Logistics has become an integral part of economic activity, with new formats such as front warehouses and hourly delivery demanding real-time visibility and rapid response. Minute-level road speed prediction is essential for platoon control, routing, and signal optimization, yet remains challenging due to heterogeneous and noisy data sources, highly coupled spatio-temporal interactions, and frequent distribution shifts. This paper proposes a Deep Operator Network–based framework that links logistics demand with traffic states. Warehouse and customer data are projected onto a five-kilometer subnetwork, generating six scenarios and about 1.2 million link–time samples. The proposed model decouples historical speeds in the branch from exogenous states in the trunk, allowing boundary changes to be incorporated as functional inputs rather than requiring retraining. Experiments demonstrate that the proposed method outperforms both classical regression and deep learning baselines, while ablation analyses verify robustness and interpretability. These findings establish operator learning as a promising direction for adaptive logistics forecasting.