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GPoM (version 1.4)

Generalized Polynomial Modelling

Description

Platform dedicated to the Global Modelling technique. Its aim is to obtain ordinary differential equations of polynomial form directly from time series. It can be applied to single or multiple time series under various conditions of noise, time series lengths, sampling, etc. This platform is developped at the Centre d'Etudes Spatiales de la Biosphere (CESBIO), UMR 5126 UPS/CNRS/CNES/IRD, 18 av. Edouard Belin, 31401 TOULOUSE, FRANCE. The developments were funded by the French program Les Enveloppes Fluides et l'Environnement (LEFE, MANU, projets GloMo, SpatioGloMo and MoMu). The French program Defi InFiNiTi (CNRS) and PNTS are also acknowledged (projects Crops'IChaos and Musc & SlowFast). The method is described in the article : Mangiarotti S. and Huc M. (2019) .

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Version

Install

install.packages('GPoM')

Monthly Downloads

168

Version

1.4

License

CeCILL-2

Maintainer

Mireille Huc

Last Published

June 16th, 2023

Functions in GPoM (1.4)

A list providing the description of six models tested by the function autoGPoMoTest.

Computes the successive derivatives of a time series

autoGPoMoSearch

Automatic search of polynomial Equations

Provides the number of polynomial terms pMax given dMax and nVar

Concat Concatenates separated time series

combiEq : Combine Equations from different sources

cano2M : Converts a model in canonical form into a matrix form

ConcatMulTS Concatenates separated time series (of single or multiples variables)

Tests the numerical integrability of models and classify their dynamical regime

Builds the derivative filter

data_vignetteVI data set

Output of the vignette VI_Sensitivity

drvSucc : Computes the successive derivatives of a time series

Find all possible sets of equation combinations considering an ensemble of possible equation.

extractEq : Extracts Equations from one system

derivODEwMultiX

deriveODEwMultiX : A Subfonction for the numerical integration of polynomial equations in the generic form defined by function poLabs and with External Forcing F(t)

data_vignetteIII data set

Output of the vignette III_Modelling

data_vignetteVII data set

Output of the vignette VII_Retro-Modelling

A subfonction for the numerical integration of polynomial equations provided in a generic form following the convetion defined by function poLabs.

Generalized Polynomial Modeling

Polynomial labels order

Model stationnary testing

For parameter Identification

Generates time series of deterministic-behavior with stochatic perturbations (measurement and/or dynamical noise)

Global Model Identification

For the numerical integration of ordinary differential equations with dynamical noise.

Numerical Integration polynomial ODEs with Multiple eXternal forcing

Estimate the models performance obtained with GPoMo in term of predictability

detectP1limCycl

Detection of limit cycles of period-1

Numerical Integration of models in ODE of polynomial form

p2dMax : provides the maximum polynomial degree dMax given the number of variables nVar and the number of possible polynomial terms pMax.

A data set for the global modeling of time series in association

Periodic solution test

subSysD : Sub-systems Disentangling

Displays the models Equations

Generate the conventional order for polynomial terms in a the polynomial formulation

Weighted inner product

visuOutGP : get a quick information of gPoMo output

Estimates the monomial time series

A data set for testing periodicity

GPoM package: Generalized Polynomial Modelling

Gram-Schmidt procedure

Rossler-1976 data set

Time series of the Rossler-1976 system

allMod_nVar3_dMax2 data set

Numerical description of a list of eighteen three-dimensional chaotic sytems (see vignette 7_Retro-Modelling)

A time series of vegetation index measured from satellite

Twelve Rossler-1976 time series (exclusively variable \(y\))

A data set for testing periodicity

Time series resulting from the integration of a non stationary system

TSallMod_nVar3_dMax2 data set

Time series of three-dimensional chaotic sytems (for vignette VII_Retro-Modelling)