jerrycxj / DDE

Data-Driven Encoding

This repository contains the source code for the paper "Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operator" (https://arxiv.org/abs/2301.06542).

The pendulum folder corresponds to a physical system represented below:

In the pendulum folder, there are three subfolders, each pertaining to different data distributions mentioned in the paper. These folders are:

• gaussian: This folder contains the data for the truncated Gaussian distribution.
• uniform: This folder contains the data for the uniform distribution.
• trajectories: This folder contains the data for the trajectories.

The winchbot folder corresponds to the physical system represented below:

In the data distribution folders and in the winchbot folder, there are a few common scripts. These scripts include:

• data_DE.py: This script runs the data-driven encoding algorithm on the set of data located in the data folder of each system.
• calc_EDMD.py: This script runs the extended dynamic mode decomposition algorithm.
• gen_error_space.py: This script generates the error plots over the state space dynamic range of each method. This is not in the winchbot folder because the state space is of too high dimension to plot easily.

Additional Results

The Images folder contains additional results pertaining to the winchbot experiment, corresponding to Section V of the paper. These results include:

which is a plot of the sum of squared errors for 25 trajectories comparing both Koopman models.

which is a plot of the y position of the winchbot for a single trajectory comparing both Koopman models.