3DBMO: A TIME SERIES CANONICAL GENERATOR TO STUDY THE PSD DIMENSIONAL DEPENDENCE IN COMPLEX PHYSICAL SYSTEMS

Reservoir computing is a machine learning method that uses the response of a dynamical system to a certain input in order to solve a task. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

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A continuous rainfall model based on vine copulas

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-12-489-2015 ◽

2015 ◽

Vol 12 (1) ◽

pp. 489-524 ◽

Cited By ~ 4

Author(s):

H. Vernieuwe ◽

S. Vandenberghe ◽

B. De Baets ◽

N. E. C. Verhoest

Keyword(s):

Time Series ◽

Continuous Time ◽

Rainfall Series ◽

Two Dimensional ◽

Statistical Comparison ◽

Dimensional Dependence ◽

Rainfall Model ◽

Bivariate Dependence ◽

Vine Copulas ◽

Continuous Rainfall

Abstract. Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of two-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependencies between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modeled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.

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Experimental Nonlinear Physics

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127497001539 ◽

1997 ◽

Vol 07 (09) ◽

pp. 2003-2033 ◽

Cited By ~ 18

Author(s):

Werner Lauterborn ◽

Thomas Kurz ◽

Ulrich Parlitz

Keyword(s):

Time Series ◽

Nonlinear Oscillations ◽

Period Doubling ◽

Nonlinear Phenomena ◽

Physical Systems ◽

Current State ◽

Recent Developments ◽

Modeling Prediction ◽

Nonlinear Noise ◽

Spatio Temporal

The review gives and account of the historical development, the current state and possible future developments of experimental nonlinear physics, with emphasis on acoustics, hydrodynamics and optics. The concepts of nonlinear time-series analysis which are the basis of the analysis of experimental outcomes from nonlinear systems are explained and recent developments pertaining to such different fields as modeling, prediction, nonlinear noise reduction, detecting determinism, synchronization, and spatio-temporal time series are surveyed. An overview is given of experiments on acoustic cavitation, a field rich of nonlinear phenomena such as nonlinear oscillations, chaotic dynamics and structure formation, and one of the first physical systems to exhibit period-doubling and chaos in experiment.

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Reservoir Computing with Delayed Input for Fast and Easy Optimisation

Entropy ◽

10.3390/e23121560 ◽

2021 ◽

Vol 23 (12) ◽

pp. 1560

Author(s):

Lina Jaurigue ◽

Elizabeth Robertson ◽

Janik Wolters ◽

Kathy Lüdge

Keyword(s):

Dynamical System ◽

Time Series ◽

Hardware Implementation ◽

Time Series Prediction ◽

Reservoir Computing ◽

Machine Learning Method ◽

Physical Systems ◽

Training Scheme ◽

Additional Input ◽

Dependent Parameter

Reservoir computing is a machine learning method that solves tasks using the response of a dynamical system to a certain input. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task-dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

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