Related papers: Spectral Simulation of Functional Time Series
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
Spatio-Temporal (ST) data science, which includes sensing, managing, and mining large-scale data across space and time, is fundamental to understanding complex systems in domains such as urban computing, climate science, and intelligent…
This paper presents a practical approach for detecting non-stationarity in time series prediction. This method is called SAFE and works by monitoring the evolution of the spectral contents of time series through a distance function. This…
This paper deals with the comparison of several stationary processes with unequal sample sizes. We provide a detailed theoretical framework on the testing problem for equality of spectral densities in the bivariate case, after which the…
Irregularly sampled time series are increasingly prevalent, particularly in medical domains. While various specialized methods have been developed to handle these irregularities, effectively modeling their complex dynamics and pronounced…
Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…
The evolution of the scanning modules for scanning transmission electron microscopes (STEM) has realized the possibility to generate arbitrary scan pathways, an approach currently explored to improve acquisition speed and to reduce electron…
A numerical study of the Einstein field equations, based on the 3+1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the…
The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of…
This paper presents transient numerical simulations of hydraulic systems in engineering applications using the spectral element method (SEM). Along with a detailed description of the underlying numerical method, it is shown that the SEM…
Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally…
Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context…
In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical…
This study investigates a method to evaluate time-series datasets in terms of the performance of deep neural networks (DNNs) with state space models (deep SSMs) trained on the dataset. SSMs have attracted attention as components inside DNNs…
Real-time simulation enables the understanding of system operating conditions by evaluating simulation models of physical components running synchronized at the real-time wall clock. Leveraging the real-time measurements of comprehensive…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that…