相关论文: Data-driven reconstruction of spatiotemporal phase…

We formulate a theory for phase reduction analysis of traveling breathers in reaction--diffusion systems with spatial translational symmetry. In this formulation, the spatial and temporal phases represent the position and oscillation of a…

Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic…

In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…

Epileptic seizure activity shows complicated dynamics in both space and time. To understand the evolution and propagation of seizures spatially extended sets of data need to be analysed. We have previously described an efficient filtering…

Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the…

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…

Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about…

We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…

In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector…

System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…

Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on statistically homogeneous random…

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…

We present a novel method for the classification and reconstruction of time dependent, high-dimensional data using sparse measurements, and apply it to the flow around a cylinder. Assuming the data lies near a low dimensional manifold…

This paper concerns the data-driven sensor deployment problem in large spatiotemporal fields. Traditionally, sensor deployment strategies have been heavily dependent on model-based planning approaches. However, model-based approaches do not…