Lian Shen

Qiang Gao, Grant B. Deane, Saswata Basak et al.

Recent increases in computing power have enabled the numerical simulation of many complex flow problems that are of practical and strategic interest for naval applications. A noticeable area of advancement is the computation of turbulent, two-phase flows resulting from wave breaking and other multiphase flow processes such as cavitation that can generate underwater sound and entrain bubbles in ship wakes, among other effects. Although advanced flow solvers are sophisticated and are capable of simulating high Reynolds number flows on large numbers of grid points, challenges in data analysis remain. Specifically, there is a critical need to transform highly resolved flow fields described on fine grids at discrete time steps into physically resolved features for which the flow dynamics can be understood and utilized in naval applications. This paper presents our recent efforts in this field. In previous works, we developed a novel algorithm to track bubbles in breaking wave simulations and to interpret their dynamical behavior over time (Gao et al., 2021a). We also discovered a new physical mechanism driving bubble production within breaking wave crests (Gao et al., 2021b) and developed a model to relate bubble behaviors to underwater sound generation (Gao et al., 2021c). In this work, we applied our bubble tracking algorithm to the breaking waves simulations and investigated the bubble trajectories, bubble creation mechanisms, and bubble acoustics based on our previous works.

Kunlun Qi, Lian Shen, Li Wang

The central object in wave turbulence theory is the wave kinetic equation (WKE), which is an evolution equation for wave action density and acts as the wave analog of the Boltzmann kinetic equations for particle interactions. Despite recent exciting progress in the theoretical aspects of the WKE, numerical developments have lagged behind. In this paper, we introduce a fast Fourier spectral method for solving the WKE. The key idea lies in reformulating the high-dimensional nonlinear wave kinetic operator as a spherical integral, analogous to the classical Boltzmann collision operator. The conservation of mass and momentum leads to a double convolution structure in Fourier space, which can be efficiently handled by the fast Fourier transform (FFT), reducing the computational cost from $O(N^{3d})$ to $O(M N^d \log N)$ with $N$-frequency nodes and $M \ll N^{2d-1}$ in $d$ dimensions. We demonstrate the accuracy and efficiency of the proposed method through several numerical tests in both 2D and 3D, revealing and conjecturing some interesting and unique features of this equation.

Ziyun Zou, Yinghui Jiang, Lian Shen et al.

Spectral Graph Neural Networks effectively handle graphs with different homophily levels, with low-pass filter mining feature smoothness and high-pass filter capturing differences. When these distinct filters could naturally form two opposite views for self-supervised learning, the commonalities between the counterparts for the same node remain unexplored, leading to suboptimal performance. In this paper, a simple yet effective self-supervised contrastive framework, LOHA, is proposed to address this gap. LOHA optimally leverages low-pass and high-pass views by embracing "harmony in diversity". Rather than solely maximizing the difference between these distinct views, which may lead to feature separation, LOHA harmonizes the diversity by treating the propagation of graph signals from both views as a composite feature. Specifically, a novel high-dimensional feature named spectral signal trend is proposed to serve as the basis for the composite feature, which remains relatively unaffected by changing filters and focuses solely on original feature differences. LOHA achieves an average performance improvement of 2.8% over runner-up models on 9 real-world datasets with varying homophily levels. Notably, LOHA even surpasses fully-supervised models on several datasets, which underscores the potential of LOHA in advancing the efficacy of spectral GNNs for diverse graph structures.

Lian Shen, Zhendan Chen, Meijia Song et al.

In multimodal graph learning, graph structures that integrate information from multiple sources, such as vision and text, can more comprehensively model complex entity relationships. However, the continuous growth of their data scale poses a significant computational bottleneck for training. Graph condensation methods provide a feasible path forward by synthesizing compact and representative datasets. Nevertheless, existing condensation approaches generally suffer from performance limitations in multimodal scenarios, mainly due to two reasons: (1) semantic misalignment between different modalities leads to gradient conflicts; (2) the message-passing mechanism of graph neural networks further structurally amplifies such gradient noise. Based on this, we propose Structural Regularized Gradient Matching (SR-GM), a condensation framework for multimodal graphs. This method alleviates gradient conflicts between modalities through a gradient decoupling mechanism and introduces a structural damping regularizer to suppress the propagation of gradient noise in the topology, thereby transforming the graph structure from a noise amplifier into a training stabilizer. Extensive experiments on four multimodal graph datasets demonstrate the effectiveness of SR-GM, highlighting its state-of-the-art performance and cross-architecture generalization capabilities in multimodal graph dataset condensation.