# Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor

## Abstract

Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.

- Authors:

- Department of Chemistry, Biology and Biotechnology, University of Perugia, 06123 Perugia (Italy)
- Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu-shi, Shiga 525-8577 (Japan)
- Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454-9110 (United States)

- Publication Date:

- OSTI Identifier:
- 22402521

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABUNDANCE; CHAOS THEORY; CONVECTION; FORECASTING; FUZZY LOGIC; ILLUMINANCE; LYAPUNOV METHOD; NEURAL NETWORKS; NONLINEAR PROBLEMS; OSCILLATIONS; PHASE SPACE; PHOTOCHROMIC MATERIALS; SPECTROPHOTOMETRY; TIME-SERIES ANALYSIS; ULTRAVIOLET RADIATION

### Citation Formats

```
Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it, Gotoda, Hiroshi, Dolnik, Milos, and Epstein, Irving R.
```*Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor*. United States: N. p., 2015.
Web. doi:10.1063/1.4905458.

```
Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it, Gotoda, Hiroshi, Dolnik, Milos, & Epstein, Irving R.
```*Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor*. United States. doi:10.1063/1.4905458.

```
Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it, Gotoda, Hiroshi, Dolnik, Milos, and Epstein, Irving R. Thu .
"Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor". United States.
doi:10.1063/1.4905458.
```

```
@article{osti_22402521,
```

title = {Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor},

author = {Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it and Gotoda, Hiroshi and Dolnik, Milos and Epstein, Irving R.},

abstractNote = {Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.},

doi = {10.1063/1.4905458},

journal = {Chaos (Woodbury, N. Y.)},

number = 1,

volume = 25,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}