Characterizing Colored Noise Time Series Patterns with Deep Learning Models

Author:

Barauna Luan O.1ORCID,Rosa Reinaldo R.2ORCID,Wuensche Carlos A.3ORCID,Sautter Rubens A.1ORCID,de Santiago Júnior Valdivino A.1ORCID,Shiguemori Elcio H.4ORCID,Padua Marcelo B.5ORCID

Affiliation:

1. Applied Computing Graduate Program (CAP), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, S. J. dos Campos, SP, Brazil

2. Applied Computing Graduate Program (CAP), Av. dos Astronautas, Coordination of Applied Research and Technological Development (COPDT), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, S. J. dos Campos, SP, Brazil

3. Astrophysics Division (DAS), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, S. J. dos Campos, SP, Brazil

4. Department of Aerospace Science and Technology, Institute for Advanced Studies (IEAv), Trevo Coronel Aviador Jos e Alberto Albano do Amarante, 01, S. J. dos Campos, SP, Brazil

5. Space Geophysics Division (DGE), National Institute for Space Research (INPE), Av. dos Astronautas, 1758, S. J. dos Campos, SP, Brazil

Abstract

Motivated by the unpredictability of stochastic time series, this paper presents an alternative deep learning approach to characterize long-term stochastic fluctuation patterns. The proposed approach considers different deep neural networks (DNNs) carefully applied to [Formula: see text] noise time series. The predictive characterization of different noise patterns is determined by the respective spectral index [Formula: see text], which works as a regression-based training attribute. The study is based on synthetic canonical colored noises (white: [Formula: see text], pink: [Formula: see text], red: [Formula: see text]) and also turbulent-like pattern with [Formula: see text]. Five DNNs are used for training based on the spectral patterns of each noise class. A new Fast Fourier Transform centric loss function for training different DNNs models drives hyperparameter exploration for each model using the optuna python package, resulting in 2560 well-established unique Deep Learning Models (DLMs) for the presented methodology. The results show that a predictive characterization of the fluctuation pattern of a stochastic time series is feasible when stochastic fluctuation is the main pattern to be addressed. Considering future applications in radio astronomy, method performance and results are interpreted and discussed in a data science context.

Publisher

World Scientific Pub Co Pte Ltd

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