Recurrence plot analysis of irregularly sampled data

Özken, İbrahim; Eroğlu, Deniz; Breitenbach, Sebastian F. M.; Marwan, Norbert; Tan, Liangcheng; Tirnakli, Uğur; Kurths, Jüergen

doi:10.1103/physreve.98.052215

Cited by 33 publications

(27 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We investigate if ANN can reconstruct the nonlinear dynamics from the incomplete information.Reconstructing dynamics from an incomplete observation has practical applications in many physical, biological, and engineering problems, where the state of the system is accessible only through a sensor network. For example, in geophysics, it is not uncommon to find time series data, which contains a large amount of missing information or is irregularly sampled, due to sensor malfunction, atmospheric conditions, or physical limitations of the sensors [12,13,14]. When a priori knowledge on the physical system is available, one of the standard approaches to reconstruct the nonlinear dynamics from an incomplete data set is to design a statistical model that incorporates the physical knowledge [15,16,17].…”

mentioning

confidence: 99%

Data-driven reconstruction of nonlinear dynamics from sparse observation

Yeo

2019

Journal of Computational Physics

View full text Add to dashboard Cite

We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the universal function approximation capability of ESN, it is shown that the reconstruction problem can be formulated as a fixed-point problem, in which the trajectory of the dynamical system is a fixed point of the ESN. An under-relaxed fixed-point iteration is proposed to reconstruct the nonlinear dynamics from a sparse observation. The proposed fixed-point ESN is tested against both univariate and multivariate chaotic dynamical systems by randomly removing up to 95% of the data. It is shown that the fixed-point ESN is able to reconstruct the complex dynamics from only 5 ∼ 10% of the data. For a relatively simple non-chaotic dynamical system, the numerical experiments on a forced van der Pol oscillator show that it is possible to reconstruct the nonlinear dynamics from only 1∼2% of the data. particular, in [8,9], it is shown that ANN is capable of predicting the dynamics of a chaotic attractor. When training an ANN for the modeling of a dynamical system, it is typical to use a sufficiently long time series data, so that the ANN fully explores the phase space. Given the huge amount of training data, it is unclear whether the long-term forecast capability of ANN is due to a high dimensional interpolation in a phase space, similar to the delay-coordinate embedding [10,11], or because ANN really learns the nonlinear dynamics. As a first step to answer this question, we first consider the problem, where only a partial observation of a time series data is available. We investigate if ANN can reconstruct the nonlinear dynamics from the incomplete information.Reconstructing dynamics from an incomplete observation has practical applications in many physical, biological, and engineering problems, where the state of the system is accessible only through a sensor network. For example, in geophysics, it is not uncommon to find time series data, which contains a large amount of missing information or is irregularly sampled, due to sensor malfunction, atmospheric conditions, or physical limitations of the sensors [12,13,14]. When a priori knowledge on the physical system is available, one of the standard approaches to reconstruct the nonlinear dynamics from an incomplete data set is to design a statistical model that incorporates the physical knowledge [15,16,17]. In [18], it is shown that a high-resolution temporal dynamics can be reconstructed from a low-resolution time series data, which has a 10 times lower time resolution, by using only a subset of the governing equations. Incorporating the physics knowledge on the training of ANN, [6] proposed "physics informed neural network", which can recover the complex nonlinear dynamics from only a small fraction of the data.It is challenging to reconstruct nonlinear dynamics without having any prior knowledge on the underlying process. There are three ...

show abstract

mentioning

confidence: 99%

Data-driven reconstruction of nonlinear dynamics from sparse observation

Yeo

2019

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…In this case, the efficiency of the method is low. The application of the RP method for revealing the features in the performance of bio-systems is considered in [27]. It is noted that the reliability of the RP method is significantly influenced by the measurement conditions, the value of the time delay, the dimensionality of nesting, as well as the value of the recurrence threshold.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Construction of a method for detecting arbitrary hazard pollutants in the atmospheric air based on the structural function of the current pollutant concentrations

Sadkovyi

Поспелов²,

Andronov

et al. 2020

EEJET

View full text Add to dashboard Cite

“…A method of RP calculation for irregular measurements based on a metric space with a metric in the form of a distance between the corresponding measurements is important for applications [17]. Work [7] presents general recommendations to overcome threshold uncertainty.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Construction of the method for semi-adaptive threshold scaling transformation when computing recurrent plots

Поспелов

Rybka

Togobytska

et al. 2019

EEJET

View full text Add to dashboard Cite

Розроблено метод напiвадаптивної масштабної трансформацiї порогу, що забезпечує обчислення рекурентних дiаграм, якi адекватно вiдображають особливостi динамiки реальних складних динамiчних систем природної i технiчної сфери. Новий науковий результат полягає в розвитку теоретичної основи методу напiвадаптивної масштабної трансформацiї порогу при обчисленнi рекурентних дiаграм шляхом удосконалення лiнiйних нормованих просторiв за рахунок введення скалярного добутку векторiв. Пропонований метод трансформацiї порога забезпечує обчислення рекурентних дiаграм, якi мають пiдвищену iнформативнiстю, iнварiантнiстю щодо параметрiв вимiрюваних векторiв станiв, а також нерегулярностi вимiрювань. Перевiрка працездатностi запропонованого методу напiвадаптивної масштабної трансформацiї порогу проведена на основi експериментальних вимiрювань концентрацiй формальдегiду, амiаку та оксиду вуглецю в атмосферному повiтрi типового промислового мiста при традицiйних стацiонарних та рухомих джерелах забруднень. Отриманi результати обчислення рекурентних дiаграм з урахуванням запропонованого методу напiвадаптивної масштабної трансформацiї порогу в цiлому пiдтверджують його працездатнiсть. Встановлено, що обчислення RP при напiвадаптивнiй трансформацiї порогу для рiзних кутових розмiрiв α конуса рекурентностi, рiвних 1°, 5°, 10° i 20° свiдчить про те, що зi зменшенням кутових розмiрiв конуса точнiсть рекурентних дiаграм виявляти небезпечнi стани в динамiчних системах зростає. Експериментально встановлено, що для адекватного вiдображення рекурентних станiв реальних динамiчних систем, за допомогою обчислюваних рекурентних дiаграм, значення величини кутових розмiрiв конуса рекурентностi повиннi складати 1-5°К лючовi слова: рекурентная дiаграма, складнi динамiчнi системи, напiвадаптивна трансформацiя порога, забруднення атмосфери UDC 004.

show abstract

Recurrence plot analysis of irregularly sampled data

Cited by 33 publications

References 37 publications

Data-driven reconstruction of nonlinear dynamics from sparse observation

Data-driven reconstruction of nonlinear dynamics from sparse observation

Construction of a method for detecting arbitrary hazard pollutants in the atmospheric air based on the structural function of the current pollutant concentrations

Construction of the method for semi-adaptive threshold scaling transformation when computing recurrent plots

Contact Info

Product

Resources

About