Related papers: Detecting Regime Transitions in Dynamical Systems …
We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in…
We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws and related systems of partial differential equations.…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
In this work, a data-driven modeling framework of switched dynamical systems under time-dependent switching is proposed. The learning technique utilized to model system dynamics is Extreme Learning Machine (ELM). First, a method is…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
In this work, we introduce a generalized framework for multiscale state-space modeling that incorporates nested nonlinear dynamics, with a specific focus on Bayesian learning under switching regimes. Our framework captures the complex…
Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate…
Anomaly detection plays a crucial role in industrial settings, particularly in maintaining the reliability and optimal performance of cooling systems. Traditional anomaly detection methods often face challenges in handling diverse data…
Motion prediction is a crucial task in autonomous driving, and one of its major challenges lands in the multimodality of future behaviors. Many successful works have utilized mixture models which require identification of positive mixture…
Predicting the dynamics of complex systems is crucial for various scientific and engineering applications. The accuracy of predictions depends on the model's ability to capture the intrinsic dynamics. While existing methods capture key…
This research presents a dynamic modeling framework and parameter identification methods for describing the highly nonlinear behaviors of flexibly connected dual-AUV systems. The modeling framework is established based on the lumped mass…
In this paper we consider the machine learning (ML) task of predicting tipping point transitions and long-term post-tipping-point behavior associated with the time evolution of an unknown (or partially unknown), non-stationary, potentially…
It is increasingly the case with modern time series that many data sets of practical interest contain abrupt changes in structure. These changes may occur in complex characteristics such as the extremal dependence structure, and identifying…
This paper addresses the problem of detecting change points in the spectral density of time series, motivated by EEG analysis of seizure patients. Seizures disrupt coherence and functional connectivity, necessitating precise detection.…
Numerical Weather Prediction (NWP) has advanced significantly in recent decades but still faces challenges in accuracy, computational efficiency, and scalability. Data-driven weather models have shown great promise, sometimes surpassing…
This paper aims to identify three electrical systems: a series RLC circuit, a motor/generator coupled system, and the Duffing-Ueda oscillator. In order to obtain the system's models was used the error reduction ratio and the Akaike…
The development of robust Early Warning Signals (EWS) is necessary to quantify the risk of crossing tipping points in the present-day climate change. Classically, EWS are statistical measures based on time series of climate state variables,…
Monitoring time between events (TBE) is a critical task in industrial settings. Traditional Statistical Process Monitoring (SPM) methods often assume that TBE variables follow an exponential distribution, which implies a constant failure…
A new method of regime shift detection in the correlation coefficient is proposed. The method is designed to find multiple change-points with unknown locations in time series. It signals a possible regime shift in real time and allows for…
Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs…