Graph learning has emerged as a promising technique for multi-view clustering due to its efficiency of learning a unified graph from multiple views. Previous multi-view graph learning methods mainly try to exploit the multi-view consistency to boost learning performance. However, these methods ignore the prevalent multi-view diversity which may be induced by noise, corruptions, or even view-specific attributes. In this paper, we propose to simultaneously and explicitly leverage the multi-view consistency and the multi-view diversity in a unified framework. The consistent parts are further fused to our target graph with a clear clustering structure, on which the cluster label to each instance can be directly allocated without any postprocessing such as $k$ -means in classical spectral clustering. In addition, our model can automatically assign suitable weight for each view based on its clustering capacity. By leveraging the subtasks of measuring the diversity of graphs, integrating the consistent parts with automatically learned weights, and allocating cluster label to each instance in a joint framework, each subtask can be alternately boosted by utilizing the results of the others towards an overall optimal solution. Extensive experimental results on several benchmark multi-view datasets demonstrate the effectiveness of our model in comparison to several state-of-the-art algorithms.

Multi-view clustering can explore consensus information from multiple views and has attracted increasing attention in the past two decades. However, existing works face two major challenges: i) how to deal with the conflict between learning view-consensus information and reconstructing inconsistent viewprivate information, and ii) how to mitigate representation degeneration caused by implementing the consistency objective for multi-view data. To address these challenges, we propose a novel framework of self-weighted contrastive fusion for deep multi-view clustering (SCMVC). First, our method establishes a hierarchical feature fusion framework, effectively segregating the consistency objective from the reconstruction objective. Then, multi-view contrastive fusion is implemented via maximizing consistency expression between the view-consensus representation and global representation, fully exploring the view consistency and complementary. More importantly, we propose to measure the discrepancy between pairwise representations, and then introduce a self-weighting method, which adaptively strengthens useful views in feature fusion and weakens unreliable views, to mitigate representation degeneration. Extensive experiments on nine public datasets demonstrate that our proposed method achieves state-of-the-art clustering performance. The code is available at https://github.com/SongwuJob/SCMVC .

Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), molecular dynamics, and dynamical systems. Although traditional numerical methods like the finite difference/element method are widely used, their computational inefficiency, due to the large number of iterations required, has long been a challenge. Recently, deep learning (DL) has emerged as a promising alternative for solving PDEs, offering new paradigms beyond conventional methods. Despite the growing interest in techniques like physics-informed neural networks (PINNs), a systematic review of the diverse neural network (NN) approaches for PDEs is still missing. This survey fills that gap by categorizing and reviewing the current progress of deep NNs (DNNs) for PDEs. Unlike previous reviews focused on specific methods like PINNs, we offer a broader taxonomy and analyze applications across scientific, engineering, and medical fields. We also provide a historical overview, key challenges, and future trends, aiming to serve both researchers and practitioners with insights into how DNNs can be effectively applied to solve PDEs.