. In this paper, we present a novel and general framework for color image denoising by integrating a traditional variational approach and learningbased denoisers. Specifically, we incorporate the deep residual convolutional neural network (CNN) prior into the traditional saturation-value total variation (SVTV) based variational model to integrate the advantages of both approaches. Saturation regularization is applied to process the saturation channel of a color image, while CNN based denoiser handles the value channel of a color image. Then, the denoising process is performed in parallel on saturation channel and value channel by using saturation regularization and deep CNN prior respectively. Theoretically, we investigate the properties of the proposed model, and give a detailed discussion based on the mathematical foundation about the solution. Numerically, we formulate an efficient and effective algorithm to solve the proposed model based on the framework of alternating direction method of multipliers (ADMM). Numerical examples are presented to demonstrate that the performance of the proposed framework is competitive in terms of visual quality and some criteria such as peak signal-to-noise ratio (PSNR), structure similarity (SSIM), quaternion structural similarity (QSSIM), and feature similarity (FSIM).
PDE problems with multi-scale features present significant challenges in scientific computing. While conventional deep learning methods based on multi-layer perceptrons exhibit spectral bias in resolving multi-scale features, physics-informed Kolmogorov–Arnold networks mitigate this issue through their architectural design and show advantages in representing multi-scale physical fields. On the other hand, insights from information bottleneck theory suggest that high-resolution sampling is important for capturing multi-scale behavior, but this requirement often leads to increased computational cost. To address this issue, we propose a simple yet effective multi-resolution training-enhanced Kolmogorov–Arnold network framework, which trains the model sequentially or alternately at different resolutions. The proposed framework is validated on various forward and inverse PDE problems with multi-scale features. Numerical results indicate that this training strategy effectively reduces computational cost without sacrificing accuracy, thereby enabling the efficient solution of complex multi-scale PDE problems in both forward and inverse settings.
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning. Despite this promise, how to train PINOs efficiently and robustly remains less well-understood than the training of either data-driven neural operators or physics-informed neural networks (PINNs). To bridge this gap, we examine key components of the PINO training pipeline, including architecture design, optimizer choice, loss balancing, and collocation-point sampling strategy. We study three representative operator backbones, Deep Operator Network (DeepONet), Fourier Neural Operator (FNO), and Continuous Vision Transformer (CViT), across five diverse parametric PDE systems. Our results show that CViT provides consistently strong and stable performance across the considered benchmarks. Beyond architecture, we find that several optimization pathologies previously identified in PINN training naturally arise in PINOs, including gradient conflicts and causal violation. We also find that mitigation algorithms developed for PINNs remain effective in the PINO setting. We further compare physics-informed and data-driven training under different data regimes, revealing that a carefully designed physics-informed training pipeline can match, and in some cases, outperform purely data-driven neural operators. Taken together, these findings provide a systematic empirical understanding of the optimization challenges in PINO training and inform a practical pipeline for efficient and robust physics-informed operator learning. Code and data are available at https://github.com/NanxiiChen/PI-CViT.
Single-cell multi-omics data contain huge information of cellular states, and analyzing these data can reveal valuable insights into cellular heterogeneity, diseases, and biological processes. However, as cell differentiation & development is a continuous and dynamic process, it remains challenging to computationally model and infer cell interaction patterns based on single-cell multi-omics data. This paper presents scI2CL, a new single-cell multi-omics fusion framework based on intra- and inter-omics contrastive learning, to learn comprehensive and discriminative cellular representations from complementary multi-omics data for various downstream tasks. Extensive experiments of four downstream tasks validate the effectiveness of scI2CL and its superiority over existing peers. Concretely, in cell clustering, scI2CL surpasses eight state-of-the-art methods on four widely-used real-world datasets. In cell subtyping, scI2CL effectively distinguishes three latent monocyte cell subpopulations, which are not discovered by existing methods. Simultaneously, scI2CL is the only method that correctly constructs the cell developmental trajectory from hematopoietic stem and progenitor cells to Memory B cells. In addition, scI2CL resolves the misclassification of cell types between two subpopulations of CD4+ T cells, while existing methods fail to precisely distinguish the mixed cells. In summary, scI2CL can accurately characterize cross-omics relationships among cells, thus effectively fuses multi-omics data and learns discriminative cellular representations to support various downstream analysis tasks.
In the emerging field of urban digital twins (UDTs), advancing intelligent road inspection (IRI) vehicles with automatic road crack detection systems is essential for maintaining civil infrastructure. Over the past decade, deep learning-based road crack detection methods have been developed to detect cracks more efficiently, accurately, and objectively, with the goal of replacing manual visual inspection. Nonetheless, comprehensive comparative analyses of state-of-the-art (SoTA) deep learning techniques, especially data-fusion and label-efficient algorithms for this task, remain limited. This paper thoroughly reviews the SoTA deep learning-based algorithms, including (1) supervised, (2) unsupervised, (3) semi-supervised, and (4) weakly-supervised methods developed for road crack detection. In addition, we establish UDTIRI-Crack, a curated and standardized benchmark suite comprising 2500 images from seven public annotated datasets, and develop an online benchmark platform to provide standardized, reproducible, and extensible evaluation of algorithms. Comprehensive experiments are conducted to compare the detection performance, computational efficiency, and generalizability of public SoTA deep learning-based algorithms for road crack detection. The feasibility of foundation models and vision-language foundation models for road crack detection is further explored. Finally, the existing challenges and future development trends of deep learning-based road crack detection algorithms are discussed. We believe this review, together with the released dataset and platform, can serve as practical guidance for developing intelligent road detection vehicles with the next-generation road condition assessment systems. The benchmark UDTIRI-Crack is available at https://udtiri.com/submission/.
