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We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
This paper explores a novel data-driven approach based on recent developments in Koopman operator theory and dynamic mode decomposition (DMD) for modeling signalized intersections. Vehicular flow and queue formation on signalized…
A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian…
Real-time traffic flow prediction holds significant importance within the domain of Intelligent Transportation Systems (ITS). The task of achieving a balance between prediction precision and computational efficiency presents a significant…
Complex spatial dependencies in transportation networks make traffic prediction extremely challenging. Much existing work is devoted to learning dynamic graph structures among sensors, and the strategy of mining spatial dependencies from…
In this paper, we propose Distributed Mirror Descent (DMD) algorithm for constrained convex optimization problems on a (strongly-)connected multi-agent network. We assume that each agent has a private objective function and a constraint…
Real-time and precise traffic flow prediction is vital for the efficiency of intelligent transportation systems. Traditional methods often employ graph neural networks (GNNs) with predefined graphs to describe spatial correlations among…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Motivated by challenges in Earth mantle convection, we present a massively parallel implementation of an Eulerian-Lagrangian method for the advection-diffusion equation in the advection-dominated regime. The advection term is treated by a…
Modeling how network-level traffic flow changes in the urban environment is useful for decision-making in transportation, public safety and urban planning. The traffic flow system can be viewed as a dynamic process that transits between…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
Human mobility analysis at urban-scale requires models to represent the complex nature of human movements, which in turn are affected by accessibility to nearby points of interest, underlying socioeconomic factors of a place, and local…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Solving traffic assignment problem for large networks is computationally challenging when conventional optimization-based methods are used. In our research, we develop an innovative surrogate model for a traffic assignment when multi-class…
Traffic forecasting problem remains a challenging task in the intelligent transportation system due to its spatio-temporal complexity. Although temporal dependency has been well studied and discussed, spatial dependency is relatively less…