Prediction of wing changes in the Lorenz63

Drawing inspiration from E. Brugnago's paper on regime changes in Lorenz's model, we trained an RNN to predict the number of time steps before the next wing change using the angles between the Lypunov covariant vectors.

More precisely, if we denote $\theta_{ij}^{t}$ the angle between CLVs $i$ and $j$ at time $t$, we trained the model to predict one of the following three categories using the matrix of angles between CLVs:

$$\begin{equation} \Theta(t) = \begin{pmatrix} \theta_{12}^{t-199} & \cdots & \cdots & \theta_{12}^{t}\\\ \theta_{13}^{t-199} & \cdots & \cdots & \theta_{13}^{t}\\\ \theta_{23}^{t-199} & \cdots & \cdots & \theta_{23}^{t} \end{pmatrix} \longrightarrow \left\{ \begin{array}{ll} 0: \text{next change in less than 50 time steps} \\\ 1: \text{next change between 50 and 200 time steps} \\\ 2: \text{next change in more then 200 time steps} \end{array} \right. \end{equation}$$

Installation

The environment can be copied using the following command

conda env create --name ENVNAME --file environment.yml

Results

Once the network has been trained, we obtain 97% accuracy on the validation data.

So, given a matrix $\Theta(t)$, the network is able to provide information about the time before next change. The aim is to continue this work on intermittent chaotic systems in order to predict regime changes.

Visualisation

An example of the use of the trained network in parallel with the system dynamics can be seen executing animation.py, or more simply by executing the following command:

bash run.sh