Related papers: Phase space reconstruction for non-uniformly sampl…

In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…

We propose an outlier robust multivariate time series model which can be used for detecting previously unseen anomalous sounds based on noisy training data. The presented approach doesn't assume the presence of labeled anomalies in the…

We outline a model and algorithm to perform inference on the palaeoclimate and palaeoclimate volatility from pollen proxy data. We use a novel multivariate non-linear non-Gaussian state space model consisting of an observation equation…

In this paper we utilize techniques from the theory of non-linear dynamical systems to define a notion of embedding threshold estimators. More specifically we use delay-coordinates embeddings of sets of coefficients of the measured signal…

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces…

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders,…

Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often…

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…

Wind speed at sea surface is a key quantity for a variety of scientific applications and human activities. Due to the non-linearity of the phenomenon, a complete description of such variable is made infeasible on both the small scale and…

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…

Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns.…

A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these…

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors…

Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…

Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…

Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…

Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning,…

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument (DESI) and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time…

Multivariate time series forecasting plays a crucial role in various real-world applications. Significant efforts have been made to integrate advanced network architectures and training strategies that enhance the capture of temporal…

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…