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Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…

Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based…

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…

Graphs are an essential part of many machine learning problems such as analysis of parse trees, social networks, knowledge graphs, transportation systems, and molecular structures. Applying machine learning in these areas typically involves…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

Graph adversarial attacks are usually produced from the two perspectives of topology/structure and node feature, both of them represent the paramount characteristics learned by today's deep learning models. Although some defense…

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…

A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting…

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while…

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…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…

Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological…

Dynamic graphs with ordered sequences of events between nodes are prevalent in real-world industrial applications such as e-commerce and social platforms. However, representation learning for dynamic graphs has posed great computational…

Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs),…

Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring…

Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications…

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

Graphs are a commonly used construct for representing relationships between elements in complex high dimensional datasets. Many real-world phenomenon are dynamic in nature, meaning that any graph used to represent them is inherently…

We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…