Related papers: Model adaptive phase space reconstruction
We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range,…
Latent Space (LS) network models project the nodes of a network on a $d$-dimensional latent space to achieve dimensionality reduction of the network while preserving its relevant features. Inference is often carried out within a Markov…
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…
In the nonlinear prediction of scalar time series, the common practice is to reconstruct the state space using time-delay embedding and apply a local model on neighborhoods of the reconstructed space. The method of false nearest neighbors…
In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…
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…
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will…
Magnetic Resonance Imaging (MRI) is a widely used medical imaging technique, but its long acquisition time can be a limiting factor in clinical settings. To address this issue, researchers have been exploring ways to reduce the acquisition…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a…
A recently proposed nearest neighbor based selection of time delays for phase space reconstruction is extended to multivariate time series, with an iterative selection of variables and time delays. A case study of numerically generated…
We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…
The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of…
Predictive state representations (PSRs) offer an expressive framework for modelling partially observable systems. By compactly representing systems as functions of observable quantities, the PSR learning approach avoids using local-minima…
This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input…
In this paper, we introduce a novel approach that combines multiresolution (MR) techniques with the flux reconstruction (FR) method to accurately and effciently simulate compressible flows. We achieve further enhancements in effciency…
Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
Time-series data, such as unsteady pressure-sensitive paint (PSP) measurement data, may contain a significant amount of random noise. Thus, in this study, we investigated a noise-reduction method that combines multivariate singular spectrum…