Related papers: An Ensemble Quadratic Echo State Network for Nonli…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or…

Early warning signals (EWSs) for complex dynamical systems aim to anticipate tipping points before they occur. While signals computed from time series data, such as temporal variance, are useful for this task, they are costly to obtain in…

Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics…

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et…

Traffic flow forecasting has emerged as an indispensable mission for daily life, which is required to utilize the spatiotemporal relationship between each location within a time period under a graph structure to predict future flow.…

We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…

In recent years, spatio-temporal graph neural networks (GNNs) have attracted considerable interest in the field of time series analysis, due to their ability to capture, at once, dependencies among variables and across time points. The…

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…

Bayesian methods are increasingly being applied to parameterize mechanistic process models used in environmental prediction and forecasting. In particular, models describing ecosystem dynamics with multiple states that are linear and…

In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

Machine learning (ML) is widely used to model chaotic systems. Among ML approaches, echo state networks (ESNs) have received considerable attention due to their simple construction and fast training. However, ESN performance is highly…

The prefrontal cortex is known to be involved in many high-level cognitive functions, in particular, working memory. Here, we study to what extent a group of randomly connected units (namely an Echo State Network, ESN) can store and…

Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by…

This paper proposes a spatiotemporal graph neural network-based performance prediction algorithm to address the challenge of forecasting performance fluctuations in distributed backend systems with multi-level service call structures. The…

Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…

We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…

Within the field of complicated multivariate time series forecasting (TSF), popular techniques frequently rely on intricate deep learning architectures, ranging from transformer-based designs to recurrent neural networks. However, recent…

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…