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Graph Neural Networks have emerged as an effective machine learning tool for multi-disciplinary tasks such as pharmaceutical molecule classification and chemical reaction prediction, because they can model non-euclidean relationships between different entities. Particle crushing, as a significant field of civil engineering, describes the breakage of granular materials caused by the breakage of particle fragment bonds under the modeling of numerical simulations, which motivates us to characterize the mechanical behaviors of particle crushing through the connectivity of particle fragments with Graph Neural Networks (GNNs). However, there lacks an open-source large-scale particle crushing dataset for research due to the expensive costs of laboratory tests or numerical simulations. Therefore, we firstly generate a dataset with 45,000 numerical simulations and 900 particle types to facilitate the research progress of machine learning for particle crushing. Secondly, we devise a hybrid framework based on GNNs to predict particle crushing strength in a particle fragment view with the advances of state of the art GNNs. Finally, we compare our hybrid framework against traditional machine learning methods and the plain MLP to verify its effectiveness. The usefulness of different features is further discussed through the gradient attribution explanation w.r.t the predictions. Our data and code are released at https://github.com/doujiang-zheng/GNN-For-Particle-Crushing.

Graph Neural Networks (GNNs) have emerged as the de facto standard for representation learning on graphs, owing to their ability to effectively integrate graph topology and node attributes. However, the inherent suboptimal nature of node connections, resulting from the complex and contingent formation process of graphs, presents significant challenges in modeling them effectively. To tackle this issue, Graph Structure Learning (GSL), a family of data-centric learning approaches, has garnered substantial attention in recent years. The core concept behind GSL is to jointly optimize the graph structure and the corresponding GNN models. Despite the proposal of numerous GSL methods, the progress in this field remains unclear due to inconsistent experimental protocols, including variations in datasets, data processing techniques, and splitting strategies. In this paper, we introduce OpenGSL, the first comprehensive benchmark for GSL, aimed at addressing this gap. OpenGSL enables a fair comparison among state-of-the-art GSL methods by evaluating them across various popular datasets using uniform data processing and splitting strategies. Through extensive experiments, we observe that existing GSL methods do not consistently outperform vanilla GNN counterparts. We also find that there is no significant correlation between the homophily of the learned structure and task performance, challenging the common belief. Moreover, we observe that the learned graph structure demonstrates a strong generalization ability across different GNN models, despite the high computational and space consumption. We hope that our open-sourced library will facilitate rapid and equitable evaluation and inspire further innovative research in this field. The code of the benchmark can be found in https://github.com/OpenGSL/OpenGSL., Comment: 25 pages, 21 figures. Camera-ready version for NeurIPS Datasets and Benchmarks Track 2023

Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information processing capacities in the brain. While considerable evidence generally supports this hypothesis, non-negligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the non-triviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, i.e., ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistic techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their marginal-preserving ordinary differential equations (ODEs) to describe data perturbation and generative modeling in a unified framework. In this paper, we carefully inspect the ODE-based sampling of a popular variance-exploding SDE and reveal several intriguing structures of its sampling dynamics. We discover that the data distribution and the noise distribution are smoothly connected with a quasi-linear sampling trajectory and another implicit denoising trajectory that even converges faster. Meanwhile, the denoising trajectory governs the curvature of the corresponding sampling trajectory and its finite differences yield various second-order samplers used in practice. Furthermore, we establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the empirical score deviation. Code is available at \url{https://github.com/zju-pi/diff-sampler}., Comment: 38 pages

The key challenge for high-power delivery through optical fibers is overcoming nonlinear optical effects. To keep a smooth output beam, most techniques for mitigating optical nonlinearities are restricted to single-mode fibers. Moving out of the single-mode paradigm, we show experimentally that wavefront-shaping of coherent input light that is incident on a highly multimode fiber can increase the power threshold for stimulated Brillouin scattering (SBS) by an order of magnitude, whilst simultaneously controlling the output beam profile. The theory reveals that the suppression of SBS is due to the relative weakness of intermodal scattering compared to intramodal scattering, and to an effective broadening of the Brillouin spectrum under multimode excitation. Our method is efficient, robust, and applicable to continuous waves and pulses. This work points toward a promising route for suppressing detrimental nonlinear effects in optical fibers, which will enable further power scaling of high-power fiber systems for applications to directed energy, remote sensing, and gravitational-wave detection.

Stimulated Brillouin scattering (SBS) is an important nonlinear optical effect which can both enable and impede optical processes in guided wave systems. Highly multi-mode excitation of fibers has been proposed as a novel route towards efficient suppression of SBS in both active and passive fibers. To study the effects of multimode excitation generally, we develop a theory of SBS for arbitrary input excitations, fiber cross section geometries and refractive index profiles. We derive appropriate nonlinear coupled mode equations for the signal and Stokes modal amplitudes starting from vector optical and tensor acoustic equations. Using applicable approximations, we find an analytical formula for the SBS (Stokes) gain susceptibility, which takes into account the vector nature of both optical and acoustic modes exactly. We show that upon multimode excitation, the SBS power in each Stokes mode grows exponentially with a growth rate that depends parametrically on the distribution of power in the signal modes. Specializing to isotropic fibers we are able to define and calculate an effective SBS gain spectrum for any choice of multimode excitation. The peak value of this gain spectrum determines the SBS threshold, the maximum SBS-limited power that can be sent through the fiber. We show theoretically that peak SBS gain is greatly reduced by highly multimode excitation due to gain broadening and relatively weaker intermodal SBS gain. We demonstrate that equal excitation of the 160 modes of a commercially available, highly multimode circular step index fiber raises the SBS threshold by a factor of 6.5, and find comparable suppression of SBS in similar fibers with a D-shaped cross-section.

Temporal graphs exhibit dynamic interactions between nodes over continuous time, whose topologies evolve with time elapsing. The whole temporal neighborhood of nodes reveals the varying preferences of nodes. However, previous works usually generate dynamic representation with limited neighbors for simplicity, which results in both inferior performance and high latency of online inference. Therefore, in this paper, we propose a novel method of temporal graph convolution with the whole neighborhood, namely Temporal Aggregation and Propagation Graph Neural Networks (TAP-GNN). Specifically, we firstly analyze the computational complexity of the dynamic representation problem by unfolding the temporal graph in a message-passing paradigm. The expensive complexity motivates us to design the AP (aggregation and propagation) block, which significantly reduces the repeated computation of historical neighbors. The final TAP-GNN supports online inference in the graph stream scenario, which incorporates the temporal information into node embeddings with a temporal activation function and a projection layer besides several AP blocks. Experimental results on various real-life temporal networks show that our proposed TAP-GNN outperforms existing temporal graph methods by a large margin in terms of both predictive performance and online inference latency. Our code is available at \url{https://github.com/doujiang-zheng/TAP-GNN}., Comment: Published by IEEE Transactions on Knowledge and Data Engineering, April 2023. We have updated the latest experimental results of baselines

Researchers of temporal networks (e.g., social networks and transaction networks) have been interested in mining dynamic patterns of nodes from their diverse interactions. Inspired by recently powerful graph mining methods like skip-gram models and Graph Neural Networks (GNNs), existing approaches focus on generating temporal node embeddings sequentially with nodes' sequential interactions. However, the sequential modeling of previous approaches cannot handle the transition structure between nodes' neighbors with limited memorization capacity. Detailedly, an effective method for the transition structures is required to both model nodes' personalized patterns adaptively and capture node dynamics accordingly. In this paper, we propose a method, namely Transition Propagation Graph Neural Networks (TIP-GNN), to tackle the challenges of encoding nodes' transition structures. The proposed TIP-GNN focuses on the bilevel graph structure in temporal networks: besides the explicit interaction graph, a node's sequential interactions can also be constructed as a transition graph. Based on the bilevel graph, TIP-GNN further encodes transition structures by multi-step transition propagation and distills information from neighborhoods by a bilevel graph convolution. Experimental results over various temporal networks reveal the efficiency of our TIP-GNN, with at most 7.2\% improvements of accuracy on temporal link prediction. Extensive ablation studies further verify the effectiveness and limitations of the transition propagation module. Our code is available at \url{https://github.com/doujiang-zheng/TIP-GNN}., Comment: Published by IEEE Transactions on Neural Networks and Learning Systems, 2022

A common wisdom posits that transports of conserved quantities across clean nonintegrable quantum systems at high temperatures are diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter if the strong interaction limit is taken. Using Krylov-typicality and purification matrix-product-state methods, we establish the following observations for the strongly interacting version of the mixed-field Ising chain, a nonintegrable lattice model imitating the experimental Rydberg blockade array. Given the strict projection owing to the infinite density-density repulsion $V$, the chain's energy transport in the presence of a transverse field $g$ is superdiffusive at infinite temperature featured by an anomalous scaling exponent $\frac{3}{4}$, indicating the existence of a novel dynamical universality class. Imposing, in addition, a growing longitudinal field $h$ causes a drastic factorization of the whole Hilbert space into smaller subsectors, evidenced by the spectral parsing of the eigenstate entanglement. Being a consequence of this approximate symmetry, a superdiffusion-to-ballistic transport transition arises at $h\approx g$. Interestingly, all the above results persist for large but finite interactions and temperatures, provided that the strongly interacting condition $g,h\ll k_\textrm{B}T\ll V$ is fulfilled. Our predictions are verifiable by current experimental facilities., Comment: 5 pages, 4 figures