Nonlinear oscillator
-------------------------------------

This is one of the dynamic data sets provided with the NeurEco installation. This test case describes a Duffing oscillator governed by the following equation:

.. math:: \ddot{x} + \delta \dot{x} + \alpha x + \beta x^3 = f(t)

where:

.. math:: \delta = 0.22
.. math:: \alpha = 1
.. math:: \beta = 875

The choice of the equation parameters were made arbitrarily to give it a strong non linearity. 

| The input features are: the trajectories of :math:`f(t)`.
| The output features are: the corresponding :math:`x(t)` with added noise.
 
This test case is provided with the following files:

* Training data set containing two trajectories:

  * train_exc_1.csv: the training inputs file - part 1, :math:`750` time steps long
  * train_out_1.csv: the training targets file - part 1
  * train_exc_2.csv: the training inputs file - part 2, :math:`750` time steps long
  * train_out_2.csv: the training targets file - part 2

* Validation data set containing one trajectory:

  * valid_exc_1.csv: the validation inputs file, :math:`1501` time steps long
  * valid_out_1.csv: the validation targets file
	
* Testing data set containing one trajectory:

  * test_exc_1.csv: the testing inputs file, :math:`1501` time steps long
  * test_out_1.csv: the testing targets file

