Related papers: Parameter inference from a non-stationary unknown …

Time series imputation is one of the most challenge problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the…

Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on…

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…

Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. However, the assessment of PINNs in industrial applications…

This paper studies the identification of nonlinearly parameterized control systems in given experiments. Several identifiability criteria are established and an implementable algorithm is proposed for practicality with the convergence rate…

In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary, or locally stationary, time…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…

We present online prediction methods for time series that let us explicitly handle nonstationary artifacts (e.g. trend and seasonality) present in most real time series. Specifically, we show that applying appropriate transformations to…

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Methods for sequential decision-making are often built upon a foundational assumption that the underlying decision process is stationary. This limits the application of such methods because real-world problems are often subject to changes…