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:

\[\ddot{x} + \delta \dot{x} + \alpha x + \beta x^3 = f(t)\]

where:

\[\delta = 0.22\]
\[\alpha = 1\]
\[\beta = 875\]

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

The input features are: the trajectories of \(f(t)\).
The output features are: the corresponding \(x(t)\) 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, \(750\) time steps long

    • train_out_1.csv: the training targets file - part 1

    • train_exc_2.csv: the training inputs file - part 2, \(750\) 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, \(1501\) 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, \(1501\) time steps long

    • test_out_1.csv: the testing targets file