Related papers: NoLiTiA: An Open-Source Toolbox for Nonlinear Time…

Missing values are pervasive in large-scale time-series data, posing challenges for reliable analysis and decision-making. Many neural architectures have been designed to model and impute the complex and heterogeneous missingness patterns…

We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…

Identifying causal relationships from observational time series data is a key problem in disciplines such as climate science or neuroscience, where experiments are often not possible. Data-driven causal inference is challenging since…

Systems are commonly monitored for health and security through collection and streaming of multivariate time series. Advances in time series forecasting due to adoption of multilayer recurrent neural network architectures make it possible…

A large number of time series forecasting models including traditional statistical models, machine learning models and more recently deep learning have been proposed in the literature. However, choosing the right model along with good…

The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of…

Time series analysis is essential for comprehending the complexities inherent in various realworld systems and applications. Although large language models (LLMs) have recently made significant strides, the development of artificial general…

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

Real-world time series often exhibit complex interdependencies that cannot be captured in isolation. Global models that model past data from multiple related time series globally while producing series-specific forecasts locally are now…

Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…

We introduce a modified algorithm to perform nonlinear filtering of a time series by locally linear phase space projections. Unlike previous implementations, the algorithm can be used not only for a posteriori processing but includes the…

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…

Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…

KnowIt (Knowledge discovery in time series data) is a flexible framework for building deep time series models and interpreting them. It is implemented as a Python toolkit, with source code and documentation available from…

Decision explanations of machine learning black-box models are often generated by applying Explainable AI (XAI) techniques. However, many proposed XAI methods produce unverified outputs. Evaluation and verification are usually achieved with…

Modern time series classifiers display impressive predictive capabilities, yet their decision-making processes mostly remain black boxes to the user. At the same time, model-agnostic explainers, such as the recently proposed SHAP, promise…

Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…