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Unsupervised graph representation learning aims to distill various graph information into a downstream task-agnostic dense vector embedding. However, existing graph representation learning approaches are designed mainly under the node…
We present an innovative framework for traffic dynamics analysis using High-Order Evolving Graphs, designed to improve spatio-temporal representations in autonomous driving contexts. Our approach constructs temporal bidirectional bipartite…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
Graph Convolution Networks (GCN) are widely used in learning graph representations due to their effectiveness and efficiency. However, they suffer from the notorious over-smoothing problem, in which the learned representations of densely…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
Traditional machine learning methods heavily rely on the independent and identically distribution assumption, which imposes limitations when the test distribution deviates from the training distribution. To address this crucial issue,…
Formation mechanisms are fundamental to the study of complex networks, but learning them from observations is challenging. In real-world domains, one often has access only to the final constructed graph, instead of the full construction…
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…
This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is…
Surrogate models are essential in structural analysis and optimization. We propose a heterogeneous graph representation of stiffened panels that accounts for geometrical variability, non-uniform boundary conditions, and diverse loading…
This paper focuses on representation learning for dynamic graphs with temporal interactions. A fundamental issue is that both the graph structure and the nodes own their own dynamics, and their blending induces intractable complexity in the…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…
In this paper, we propose a general framework for constructing tight framelet systems on graphs with localized supports based on partition trees. Our construction of framelets provides a simple and efficient way to obtain the orthogonality…
Neurons exhibit intricate geometries within their neurite networks, which play a crucial role in processes such as signaling and nutrient transport. Accurate simulation of material transport in the networks is essential for understanding…
Ionic models, the set of ordinary differential equations (ODEs) describing the time evolution of the state of excitable cells, are the cornerstone of modeling in neuro- and cardiac electrophysiology. Modern ionic models can have tens of…
Continuous-depth graph neural networks, also known as Graph Neural Differential Equations (GNDEs), combine the structural inductive bias of Graph Neural Networks (GNNs) with the continuous-depth architecture of Neural ODEs, offering a…
Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models…
Hypergraphs, as a generalization of traditional graphs, naturally capture high-order relationships. In recent years, hypergraph neural networks (HNNs) have been widely used to capture complex high-order relationships. However, most existing…
Hypergraph data, which capture multi-way interactions among entities, are increasingly prevalent in the big data era. Generating new hyperlinks from an observed, usually high-dimensional hypergraph is an important yet challenging task with…