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Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…
Threshold models and their dynamics may be used to model the spread of `behaviors' in social networks. Regarding such from a modal logical perspective, it is shown how standard update mechanisms may be emulated using action models -- graphs…
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of…
This paper presents a novel application of graph neural networks for modeling and estimating network heterogeneity. Network heterogeneity is characterized by variations in unit's decisions or outcomes that depend not only on its own…
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…
GFlowNets is a novel flow-based method for learning a stochastic policy to generate objects via a sequence of actions and with probability proportional to a given positive reward. We contribute to relaxing hypotheses limiting the…
We introduce a rigorous framework for stochastic cell transmission models for general traffic networks. The performance of traffic systems is evaluated based on preference functionals and acceptable designs. The numerical implementation…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Graph neural networks, recently introduced into the field of fluid flow surrogate modeling, have been successfully applied to model the temporal evolution of various fluid flow systems. Existing applications, however, are mostly restricted…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
This paper proposes a novel approach using Graph Neural Networks (GNNs) to solve the AC Power Flow problem in power grids. AC OPF is essential for minimizing generation costs while meeting the operational constraints of the grid.…
Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…
Accurate electricity demand forecasting is essential for several reasons, especially as the integration of renewable energy sources and the transition to a decentralized network paradigm introduce greater complexity and uncertainty. The…
Urban wind flow modeling and simulation play an important role in air quality assessment and sustainable city planning. A key challenge for modeling and simulation is handling the complex geometries of the urban landscape. Low order models…
The chapter aims to explore the application of graph theory and networks in the recommendation domain, encompassing the mathematical models that form the foundation for the algorithms and recommendation systems developed based on them. The…
Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide…
In recent years, with the rapid enhancement of computing power, deep learning methods have been widely applied in wireless networks and achieved impressive performance. To effectively exploit the information of graph-structured data as well…