Model Reconstruction

This repository provides advanced utility to analyze n-dimensional systems and reconstruct them from its time series.

reconstructionutils.py

Use this library to create reconstructed models from your time series. simply type:

import reconstructionutils as ru

# set up your systems time series
series = [z_1, z_2, ..., z_n]

# create a model instance
system = ru.Model(series, 6)

# create a model and reconstruct your system
res = system.evaluate()

TODO:

• take the mean as defined in arithmetic mean in reconstructionutils.Model._retrieve_fit_coefficients
• using np.gradient for derivative in reconstructionutils.Model.__init__

stanpy.py

View flemk/ModelReconstruction for examples using this module.

This module provides a class to determine drift- and diffusion-coefficients of n-dimensional time series by using their statistical definition.

import stanpy as sp

time_series = [[1, 2, ...], [1, 2, ...]] # your time seres you want to analyze

analysis = sp.StochasticAnalysis(time_series)
analysis.analyze()

# drift and diffusion coefficients are now stored in:
analysis.drift()
analysis.diffusion()

# in the 2d case you can visualize them builtin:
analysis.visualize_2d()

# and you can reconstruct your series with choosen initial values:
r = analysis.reconstruct()

# by converting your coefficients into a FPE you might gain more insight:
f = analysis.solve_fpe()

cutility.py

Math's helper function are stored in this module. Featuring finite differences and upwind schemes as well as mulitdimensional polynominal exponents.