Parallel implementations of the False Nearest Neighbors method to study the behavior of dynamical models

• Published in: Mathematical and computer modelling 2010-10, Vol.52 (7), p.1237-1242
• Main Authors: Marín Carrión, I., Arias Antúnez, E., Artigao Castillo, M.M., Miralles Canals, J.J.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Geometry; Mathematical analysis; Mathematics; Message-passing interface; Methods of scientific computing (including symbolic computation, algebraic computation); Nonlinear time series analysis; Numerical analysis. Scientific computation; Parallel computing; Physics; POSIX threads; Sciences and techniques of general use; The False Nearest Neighbors method
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2010.03.025

Dynamical models are an issue of multidisciplinary studies with direct applications in different areas of science and technology (medicine, oceanography, economics, biology, etc.). One way to study dynamical models is through their associated time series in order to find out the model evolution (equilibrium points, orbits, trajectories, etc.) and determine intervals where the predictions are reliable. A key point in this process is the computing of the time series embedding dimension using the False Nearest Neighbors (FNN) method. The FNN method has a high computational cost when long time series are available (or used), so the execution time has to be reduced. This paper describes two parallel implementations of the FNN method for hybrid (shared and distributed) memory architectures. To the best of the authors’ knowledge, the hybrid implementations presented in this paper represent the first parallel implementation of this type. Moreover, considering a hybrid implementation makes it possible to take advantage of different parallel architectures, because knowing the numbers of nodes and the number of cores per node, the software is autotuned in order to exploit the maximum degree of parallelism existing in the target machine. The computationally intensive part of the method lies mainly in the neighbor search and therefore this task is parallelized and executed using 2 to 64 processors. The accuracy and performance of the two parallel approaches are then assessed and compared against the best sequential implementation of the FNN method which appears in the TISEAN project.