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

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]. 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.