Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing

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Description:

option = option of running the baseline (0) or our algorithm (1) (see the paper in Reference below)

n_ens = number of networks independently trained for ensemble learning (denoted in the paper)

trainlen + 1 = length of accessible/given time series (denoted +1 in the paper)

valid = length of validation time series (denoted in the paper)

future = length of predicted time series (denoted in the paper)

trainbeg = index indicating the initial time (denoted in the paper) on which the given time series runs

num_layer = number of layer in the network (denoted +1 in the paper)

dt = time step used in numerical integration generating the time series data (denoted in the paper)

so that length of time series used for training in the case of option = 0 is trainlen - valid + 1 and that in the case of option = 1 is trainlen - valid

Hyperparameter grid search:

For hyperparameters in the first layer of network:

• dimension of reservoir hidden states is selected from the interval [n_res_start_1, n_res_start_1 + n_res_total * n_res_delta_1)

• spectral radius is selected from the interval [spec_rad_start_1, spec_rad_start_1 + spec_rad_total * spec_rad_delta_1)

• sparsity level is selected from the interval [sparsity_start_1, sparsity_start_1 + sparsity_total * sparsity_delta_1)

• noise level is selected from the interval [noise_start, noise_start + noise_total * noise_delta)

and similarly for the hyperparameters in the second layer and so on

If needed, discard an initial transient by disregarding the first n_transient reservoir hidden states

Examples:

• Here is an example to run the algorithm on the time series of Example 1:

python3 driver.py --name Example1 --option 1 --n_ens 50 --trainlen 3700 --valid 10 --future 400 --trainbeg 0 --num_layer 1 --n_res_start_1 600 --n_res_delta_1 20 --n_res_total 8 --spec_rad_start_1 0.7 --spec_rad_delta_1 0.1 --spec_rad_total 1 --sparsity_start_1 0.1 --sparsity_delta_1 0.1 --sparsity_total 1 --noise_start 0.001 --noise_delta 0.001 --noise_total 1

• Here is an example to run the algorithm on the time series of Example 2:

python3 driver.py --name Example2 --option 1 --n_ens 50 --trainlen 9410 --valid 4 --future 590 --trainbeg 0 --num_layer 3 --n_res_start_1 100 --n_res_delta_1 50 --n_res_start_2 100 --n_res_delta_2 50 --n_res_start_3 100 --n_res_delta_3 50 --n_res_total 5 --spec_rad_start_1 0.6 --spec_rad_delta_1 0.05 --spec_rad_start_2 0.7 --spec_rad_delta_2 0.05 --spec_rad_start_3 0.8 --spec_rad_delta_3 0.05 --spec_rad_total 1 --sparsity_start_1 0.05 --sparsity_delta_1 0.05 --sparsity_start_2 0.05 --sparsity_delta_2 0.05 --sparsity_start_3 0.05 --sparsity_delta_3 0.05 --sparsity_total 1 --noise_start 0.003 --noise_delta 0.003 --noise_total 1

• Here is an example to run the algorithm on the time series of Example 3:

python3 driver.py --name Example3 --option 1 --n_ens 50 --trainlen 8233 --valid 5 --future 37 --trainbeg 200 --num_layer 1 --n_res_start_1 500 --n_res_delta_1 50 --n_res_total 7 --spec_rad_start_1 0.95 --spec_rad_delta_1 0.05 --spec_rad_total 1 --sparsity_start_1 0.1 --sparsity_delta_1 0.05 --sparsity_total 1 --noise_start 0.003 --noise_delta 0.001 --noise_total 1 --n_transient 100

• Here is an example to run the algorithm on other time series not studied in the paper (using option = 0, for standardized data of Nino-3 index):

python3 driver.py --name Other --n_ens 20 --trainlen 1600 --valid 3 --future 6 --trainbeg 100 --num_layer 1 --n_res_start_1 100 --n_res_delta_1 50 --n_res_total 11 --spec_rad_start_1 0.9 --spec_rad_delta_1 0.1 --spec_rad_total 1 --sparsity_start_1 0.1 --sparsity_delta_1 0.1 --sparsity_total 1 --noise_start 0.001 --noise_delta 0.001 --noise_total 1 --option 0

Reference

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For more details, please refer to the paper:

• ArXiv: https://arxiv.org/abs/1908.03771

• Journal: Chaos: An Interdisciplinary Journal of Nonlinear Science (2020); doi: 10.1063/5.0023764