Partial Differential Equations (PDEs) are fundamental to the mathematical modeling of a wide range of physical, biological, and engineering systems. These systems span diverse fields, such as fluid dynamics, heat transfer, structural mechanics, and population dynamics. Traditionally, numerical methods such as Finite Difference Method (FDM), Finite Volume Method (FVM), Finite Element Method (FEM) [Smith, 1985, Zienkiewicz et al., 2005], and spectral methods have been employed to obtain approximate solutions to PDEs. Although these methods are highly effective, they ultimately reduce to solving linear systems of equations. This often leads to several challenges, such as when solving high-dimensional problems or performing adaptive solutions for complex domains.

Dynamic Graph Neural Networks (DGNNs) have gained widespread attention due to their applicability in diverse domains such as traffic network prediction, epidemiological forecasting, and social network analysis. In this paper, we present ReInc, a system designed to enable efficient and scalable training of DGNNs on large-scale graphs. ReInc introduces key innovations that capitalize on the unique combination of Graph Neural Networks (GNNs) and Recurrent Neural Networks (RNNs) inherent in DGNNs. By reusing intermediate results and incrementally computing aggregations across consecutive graph snapshots, ReInc significantly enhances computational efficiency. To support these optimizations, ReInc incorporates a novel two-level caching mechanism with a specialized caching policy aligned to the DGNN execution workflow. Additionally, ReInc addresses the challenges of managing structural and temporal dependencies in dynamic graphs through a new distributed training strategy. This approach eliminates communication overheads associated with accessing remote features and redistributing intermediate results. Experimental results demonstrate that ReInc achieves up to an order of magnitude speedup compared to state-of-the-art frameworks, tested across various dynamic GNN architectures and real-world graph datasets.

We introduce a novel Dynamic Graph Neural Network (DGNN) architecture for solving conditional $m$-steps ahead forecasting problems in temporal financial networks. The proposed DGNN is validated on simulated data from a temporal financial network model capturing stylized features of Interest Rate Swaps (IRSs) transaction networks, where financial entities trade swap contracts dynamically and the network topology evolves conditionally on a reference rate. The proposed model is able to produce accurate conditional forecasts of net variation margins up to a $21$-day horizon by leveraging conditional information under pre-determined stress test scenarios. Our work shows that the network dynamics can be successfully incorporated into stress-testing practices, thus providing regulators and policymakers with a crucial tool for systemic risk monitoring.

Graph unlearning has emerged as an essential tool for safeguarding user privacy and mitigating the negative impacts of undesirable data. Meanwhile, the advent of dynamic graph neural networks (DGNNs) marks a significant advancement due to their superior capability in learning from dynamic graphs, which encapsulate spatial-temporal variations in diverse real-world applications (e.g., traffic forecasting). With the increasing prevalence of DGNNs, it becomes imperative to investigate the implementation of dynamic graph unlearning. However, current graph unlearning methodologies are designed for GNNs operating on static graphs and exhibit limitations including their serving in a pre-processing manner and impractical resource demands. Furthermore, the adaptation of these methods to DGNNs presents non-trivial challenges, owing to the distinctive nature of dynamic graphs. To this end, we propose an effective, efficient, model-agnostic, and post-processing method to implement DGNN unlearning. Specifically, we first define the unlearning requests and formulate dynamic graph unlearning in the context of continuous-time dynamic graphs. After conducting a role analysis on the unlearning data, the remaining data, and the target DGNN model, we propose a method called Gradient Transformation and a loss function to map the unlearning request to the desired parameter update. Evaluations on six real-world datasets and state-of-the-art DGNN backbones demonstrate its effectiveness (e.g., limited performance drop even obvious improvement) and efficiency (e.g., at most 7.23$\times$ speed-up) outperformance, and potential advantages in handling future unlearning requests (e.g., at most 32.59$\times$ speed-up).

The upcoming landscape of Earth Observation missions will defined by networked heterogeneous nanosatellite constellations required to meet strict mission requirements, such as revisit times and spatial resolution. However, scheduling satellite communications in these satellite networks through efficiently creating a global satellite Contact Plan (CP) is a complex task, with current solutions requiring ground-based coordination or being limited by onboard computational resources. The paper proposes a novel approach to overcome these challenges by modeling the constellations and CP as dynamic networks and employing graph-based techniques. The proposed method utilizes a state-of-the-art dynamic graph neural network to evaluate the performance of a given CP and update it using a heuristic algorithm based on simulated annealing. The trained neural network can predict the network delay with a mean absolute error of 3.6 minutes. Simulation results show that the proposed method can successfully design a contact plan for large satellite networks, improving the delay by 29.1%, similar to a traditional approach, while performing the objective evaluations 20x faster.

Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution operation by using both attribute and structure information through coupled learning. In essence, GNNs, from an optimization perspective, seek to learn a consensus and compromise embedding representation that balances attribute and graph information, selectively exploring and retaining valid information. To obtain a more comprehensive embedding representation of nodes, a novel GNNs framework, dubbed Decoupled Graph Neural Networks (DGNN), is introduced. DGNN explores distinctive embedding representations from the attribute and graph spaces by decoupled terms. Considering that semantic graph, constructed from attribute feature space, consists of different node connection information and provides enhancement for the topological graph, both topological and semantic graphs are combined for the embedding representation learning. Further, structural consistency among attribute embedding and graph embeddings is promoted to effectively remove redundant information and establish soft connection. This involves promoting factor sharing for adjacency reconstruction matrices, facilitating the exploration of a consensus and high-level correlation. Finally, a more powerful and complete representation is achieved through the concatenation of these embeddings. Experimental results conducted on several graph benchmark datasets verify its superiority in node classification task.

Dynamic graph data mining has gained popularity in recent years due to the rich information contained in dynamic graphs and their widespread use in the real world. Despite the advances in dynamic graph neural networks (DGNNs), the rich information and diverse downstream tasks have posed significant difficulties for the practical application of DGNNs in industrial scenarios. To this end, in this paper, we propose to address them by pre-training and present the Contrastive Pre-Training Method for Dynamic Graph Neural Networks (CPDG). CPDG tackles the challenges of pre-training for DGNNs, including generalization capability and long-short term modeling capability, through a flexible structural-temporal subgraph sampler along with structural-temporal contrastive pre-training schemes. Extensive experiments conducted on both large-scale research and industrial dynamic graph datasets show that CPDG outperforms existing methods in dynamic graph pre-training for various downstream tasks under three transfer settings.

Dynamic graph neural network (DGNN) is becoming increasingly popular because of its widespread use in capturing dynamic features in the real world. A variety of dynamic graph neural networks designed from algorithmic perspectives have succeeded in incorporating temporal information into graph processing. Despite the promising algorithmic performance, deploying DGNNs on hardware presents additional challenges due to the model complexity, diversity, and the nature of the time dependency. Meanwhile, the differences between DGNNs and static graph neural networks make hardware-related optimizations for static graph neural networks unsuitable for DGNNs. In this paper, we select eight prevailing DGNNs with different characteristics and profile them on both CPU and GPU. The profiling results are summarized and analyzed, providing in-depth insights into the bottlenecks of DGNNs on hardware and identifying potential optimization opportunities for future DGNN acceleration. Followed by a comprehensive survey, we provide a detailed analysis of DGNN performance bottlenecks on hardware, including temporal data dependency, workload imbalance, data movement, and GPU warm-up. We suggest several optimizations from both software and hardware perspectives. This paper is the first to provide an in-depth analysis of the hardware performance of DGNN Code is available at https://github.com/sharc-lab/DGNN_analysis.

Link prediction on dynamic graphs is an important task in graph mining. Existing approaches based on dynamic graph neural networks (DGNNs) typically require a significant amount of historical data (interactions over time), which is not always available in practice. The missing links over time, which is a common phenomenon in graph data, further aggravates the issue and thus creates extremely sparse and dynamic graphs. To address this problem, we propose a novel method based on the neural process, called Graph Sequential Neural ODE Process (GSNOP). Specifically, GSNOP combines the advantage of the neural process and neural ordinary differential equation that models the link prediction on dynamic graphs as a dynamic-changing stochastic process. By defining a distribution over functions, GSNOP introduces the uncertainty into the predictions, making it generalize to more situations instead of overfitting to the sparse data. GSNOP is also agnostic to model structures that can be integrated with any DGNN to consider the chronological and geometrical information for link prediction. Extensive experiments on three dynamic graph datasets show that GSNOP can significantly improve the performance of existing DGNNs and outperform other neural process variants.

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent advances in generative networks, identifying the image generation mechanism still remains challenging. In this paper, we present an explorative sampling algorithm to analyze generation mechanism of DGNNs. Our method efficiently obtains samples with identical attributes from a query image in a perspective of the trained model. We define generative boundaries which determine the activation of nodes in the internal layer and probe inside the model with this information. To handle a large number of boundaries, we obtain the essential set of boundaries using optimization. By gathering samples within the region surrounded by generative boundaries, we can empirically reveal the characteristics of the internal layers of DGNNs. We also demonstrate that our algorithm can find more homogeneous, the model specific samples compared to the variations of {\epsilon}-based sampling method.