Overview This dataset contains input-output data of a damped nonlinear pendulum that is actuated at the mounting point. The data was generated with statesim [1], a python package for simulating linear and nonlinear ODEs, for the system actuated pendulum. The configuration .json 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 raw folder. Then, they are split into subsets for training, testing, and validation and can be found in the processed folder; details about the splitting are found in the config.json file.

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.

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

Input generation Input trajectories are sampled from a multivariate-normal distribution.

Noise Gaussian white noise of approximately 30dB is added at the output.

Statistics The input and output size is one.

In-distribution data: 2 100 000 data points

        Training: 10 000 trajectories of length 150
        Validation: 2 000 trajectories of length 150
        Test: 2 000 trajectories of length 150


Out-of-distribution data: 7 times 100 000 data points
    7 different datasets were only used for testing. Each dataset contains 200 trajectories of length 500.



References

    Frank, D. statesim [Computer software]. https://github.com/Dany-L/statesim
    Lu, L., Jin, P., Pang, G., Zhang, Z., & Karniadakis, G. E. (2021). Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature machine intelligence, 3(3), 218-229.