Related papers: Edge-indexed network time series with graph Ornste…

Network structures in various backgrounds play important roles in social, technological, and biological systems. However, the observable network structures in real cases are often incomplete or unavailable due to measurement errors or…

This study presents a framework for predicting unsteady transonic wing pressure distributions, integrating an autoencoder architecture with graph convolutional networks and graph-based temporal layers to model time dependencies. The…

Graph neural networks (GNNs) have emerged as a state-of-the-art data-driven tool for modeling connectivity data of graph-structured complex networks and integrating information of their nodes and edges in space and time. However, as of yet,…

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations…

Traditional optimization-based techniques for time-synchronized state estimation (SE) often suffer from high online computational burden, limited phasor measurement unit (PMU) coverage, and presence of non-Gaussian measurement noise.…

Lognormality was found experimentally for coarse-grained squared turbulence velocity and velocity increment when the coarsening scale is comparable to the correlation scale of the velocity (Mouri et al. Phys. Fluids 21, 065107, 2009). We…

Volatility forecasting is essential for risk management and decision-making in financial markets. Traditional models like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) effectively capture volatility clustering but often…

Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity…

Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with Gaussian driving noise $ Y_t^{(1)} := \int^t_0…

This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent…

We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…

Let the Ornstein-Uhlenbeck process $(X_t)_{t\ge0}$ driven by a fractional Brownian motion $B^{H }$, described by $dX_t = -\theta X_t dt + \sigma dB_t^{H }$ be observed at discrete time instants $t_k=kh$, $k=0, 1, 2, \cdots, 2n+2 $. We…

Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…

We deal with a complex-valued Ornstein-Uhlenbeck (OU) process with parameter $\lambda\in\mathbb{R}$starting from a point different from 0 and the way that it winds around the origin.The starting point of this paper is the skew product…

Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau…

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its…

Session-based recommendation (SBR) aims to predict the user next action based on the ongoing sessions. Recently, there has been an increasing interest in modeling the user preference evolution to capture the fine-grained user interests.…

The regression of multiple inter-connected sequence data is a problem in various disciplines. Formally, we name the regression problem of multiple inter-connected data entities as the "dynamic network regression" in this paper. Within the…

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables…