Related papers: Measure-Theoretic Time-Delay Embedding
The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…
We suggest an algorithm for determining the proper delay time and the minimum embedding dimension for Takens' delay-time embedding procedure. This method resorts to the rate of change of the spatial distribution of points on a reconstructed…
Shroer, Sauer, Ott and Yorke conjectured in 1998 that the Takens delay embedding theorem can be improved in a probabilistic context. More precisely, their conjecture states that if $\mu$ is a natural measure for a smooth diffeomorphism of a…
A new and accurate method to determine the time delay and embedding dimension for state space reconstruction of a high dimensional system from a scalar time series using time delay embedding is presented. The time delay is obtained to…
In this paper, we deal with the problem of the stabilization in the sample-and-hold sense, by emulation of continuous-time, observer-based, global stabilizers. Fully nonlinear time-delay systems are studied. Sufficient conditions are…
A gedanken-experiment is proposed for `weighing'' the total mass of a closed system from within the system. We prove that for an internal observer the time $\tau$, required to measure the total energy with accuracy $\Delta E$, is bounded…
We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…
Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…
Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's…
Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently, neural dynamics modeling method have become a prevalent…
We propose a novel approach for performing dynamical system identification, based upon the comparison of simulated and observed physical invariant measures. While standard methods adopt a Lagrangian perspective by directly treating…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…
We analyze the popular ``state-space'' class of algorithms for detecting casual interaction in coupled dynamical systems. These algorithms are often justified by Takens' embedding theorem, which provides conditions under which relationships…
The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…
Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…