This repository shows an example of using machine learning strategy to predict extreme events in complex systems: A densely connected multi-scale network model (MS-D Net) is applied to capture the extreme events appearing in a truncated Korteweg–de Vries (tKdV) statistical framework which generates transition from near-Gaussian statistics to anomalous skewed distributions consistent with recent laboratory experiments for shallow water waves across an abrupt depth change.

The main.py script is used to run the experiment. To train the neural network model without using a pretrained checkpoint, run the following command:

python main.py --exp_dir=<EXP_DIR> --cfg=<CONFIG_PATH> --nopretrained --write_data --train

To test the trained model with the path to the latest checkpoint, run the following command:

python main.py --exp_dir=<EXP_DIR> --cfg=<CONFIG_PATH> --pretrained --write_data --notrain

Datasets for training and prediction in the neural network model are generated from direct numerical simulations of the tKdV equation in different statistical regimes:

• training dataset 'tKdV_J32th10': model with truncation size $J=32$ and inverse temperature $\theta = -0.1$, showing near-Gaussian statistics in solutions;
• prediction dataset 'tKdV_J32th50': model with truncation size $J=32$ and inverse temperature $\theta = -0.5$, showing highly skewed statistics in solutions.

Different datasets can be tested by changing the configuration file, config.py. A wider variety of problems in different statistical regimes can be also tested by adding new corresponding dataset into the data/ folder.

• PyTorch >= 1.2.0

[1] D. Qi and A. J. Majda, “Using machine learning to predict extreme events in complex systems,” Proceedings of the National Academy of Sciences, 2019.
[2] A. J. Majda, M. Moore, and D. Qi, “Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change,” Proceedings of the National Academy of Sciences, vol. 116, no. 10, pp. 3982–3987, 2019.