arXiv:2603.22309v1 Announce Type: cross Abstract: Partial differential equation (PDE) simulation holds extensive significance in scientific research. Currently, the integration of deep neural networks to learn solution operators of PDEs has introduced great potential. In this paper, we present UniFluids, a conditional flow-matching framework that harnesses the scalability of diffusion Transformer to unify learning of solution operators across diverse PDEs with varying dimensionality and physical variables. Unlike the autoregressive PDE foundation models, UniFluids adopts flow-matching to achieve parallel sequence generation, making it the first such approach for unified operator learning. Specifically, the introduction of a unified four-dimensional spatiotemporal representation for the heterogeneous PDE datasets enables joint training and conditional encoding. Furthermore, we find the effective dimension of the PDE dataset is much lower than its patch dimension. We thus employ $x$-prediction in the flow-matching operator learning, which is verified to significantly improve prediction accuracy. We conduct a large-scale evaluation of UniFluids on several PDE datasets covering spatial dimensions 1D, 2D and 3D. Experimental results show that UniFluids achieves strong prediction accuracy and demonstrates good scalability and cross-scenario generalization capability. The code will be released later.

arXiv:2603.22840v1 Announce Type: cross Abstract: Unsupervised anomaly detection plays a pivotal role in industrial defect inspection and medical image analysis, with most methods relying on the reconstruction framework. However, these methods may suffer from over-generalization, enabling them to reconstruct anomalies well, which leads to poor detection performance. To address this issue, instead of focusing solely on normality reconstruction, we propose an innovative Uncertainty-Integrated Anomaly Perception and Restoration Attention Network (URA-Net), which explicitly restores abnormal patterns to their corresponding normality. First, unlike traditional image reconstruction methods, we utilize a pre-trained convolutional neural network to extract multi-level semantic features as the reconstruction target. To assist the URA-Net learning to restore anomalies, we introduce a novel feature-level artificial anomaly synthesis module to generate anomalous samples for training. Subsequently, a novel uncertainty-integrated anomaly perception module based on Bayesian neural networks is introduced to learn the distributions of anomalous and normal features. This facilitates the estimation of anomalous regions and ambiguous boundaries, laying the foundation for subsequent anomaly restoration. Then, we propose a novel restoration attention mechanism that leverages global normal semantic information to restore detected anomalous regions, thereby obtaining defect-free restored features. Finally, we employ residual maps between input features and restored features for anomaly detection and localization. The comprehensive experimental results on two industrial datasets, MVTec AD and BTAD, along with a medical image dataset, OCT-2017, unequivocally demonstrate the effectiveness and superiority of the proposed method.