Damped pendulum for nonlinear system identification - inputs are sampled from a multivariate-normal distribution - synthetically generated

<h3>Overview</h3>
<p>This dataset contains input-output data of a damped nonlinear pendulum that is actuated at the mounting point. The data was generated with <code>statesim</code> [1], a python package for simulating linear and nonlinear ODEs, for the system <code>actuated pendulum</code>. The configuration <code>.json</code> files for the corresponding datasets (in-distribution and out-of-distribution) can be found in the respective folders. After creating the dataset, the files are stored in the <code>raw</code> folder. Then, they are split into subsets for training, testing, and validation and can be found in the <code>processed</code> folder; details about the splitting are found in the <code>config.json</code> file.</p>

<p> The dataset can be used to test system identification algorithms and methods that aim to identify nonlinear dynamics from input-output measurements. The training dataset is used to optimize the model parameters, the validation set for hyperparameter optimization, and the test set only for the final evaluation.</p>

<p>In [2], the authors used the same underlying dynamics to create their dataset but without damping terms.</p>

<h3>Input generation</h3>
Input trajectories are sampled from a multivariate-normal distribution.

<h3>Noise</h3>
Gaussian white noise of approximately 30dB is added at the output.

<h3>Statistics</h3>
<p>The input and output size is one.</p>
<ul>
<li>In-distribution data: 2 100 000 data points
<ul>
<li>Training: 10 000 trajectories of length 150</li>
<li>Validation: 2 000 trajectories of length 150</li>
<li>Test: 2 000 trajectories of length 150</li>
</ul>
</li>
<li>Out-of-distribution data: 7 times 100 000 data points
<p>7 different datasets were only used for testing. Each dataset contains 200 trajectories of length 500.</p>
</li>
</ul>

<h3>References</h3>
<ol>
<li>Frank, D. <em>statesim</em> [Computer software]. <a href="https://github.com/Dany-L/statesim">https://github.com/Dany-L/statesim</a></li>
<li>Lu, L., Jin, P., Pang, G., Zhang, Z., & Karniadakis, G. E. (2021). <a href="https://doi.org/10.1038/s42256-021-00302-5">Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.</a> Nature machine intelligence, 3(3), 218-229.</li>
</ol>