Gen Dynamics

A collection of datasets for learning generalisable dynamical systems

Learning dynamical systems that can generalize to various parameter changes in their underlying ODEs or PDEs is a significant but challenging task. In recent years, several methods have been proposed to learn such systems. This repository contains a collection of datasets that can be used to benchmark these methods.

We aim to provide a consistent interface to access each dataset. The datasets are made up of 4 splits each:

1. train: For In-Domain meta-learning
2. test: For In-Domain meta-testing
3. ood_train: For Out-of-Distribution adaptation to new environments
4. ood_test: For Out-of-Distribution testing of the adaptation to new environments

Each split is a NumPy archive (.npz) containing the trajectory of the system (X) and the time points (t) at which they were evaluated. While t is a 1-dimensional array, X is a 4-dimensional tensor of shape (nb_envs, nb_trajs_per_env, nb_steps_per_traj, state_size) described as follows:

1. nb_envs: Number of distinct environments
2. nb_trajs_per_env: Number of trajectories per environment
3. nb_steps_per_traj: Number of time steps per trajectory (matching the size of t)
4. state_size: Size of the state space

Methods

The following methods use at least in part the datasets provided in this repository:

• LEADS: https://arxiv.org/abs/2106.04546
• CoDA: https://arxiv.org/pdf/2202.01889.pdf
• NCF: Coming soon...
• FOCA: https://openreview.net/forum?id=AW0i0lOhzqJ
• Etc. (If you have a method that you would like to add, please open an issue, a pull request, or get in touch directly :) )

Current Datasets

• Lotka-Volterra (see CoDA, LEADS)
• Glycolytic Oscillator (see CoDA, LEADS)
• Gray-Scott: Since this is a PDE on a 2D grid, its spatial data is flattened to a 1D state vector (see CoDA, LEADS, NCF)
• Selkov-Model (see NCF)
• Simple Pendulum (see NCF) WARNING: incomplete !
• Please feel free to add more datasets by opening a pull request.

More Datasets to Add

The following datasets are currently being prepared for addition to this repository:

• https://arxiv.org/abs/2312.00477
• https://arxiv.org/abs/2303.03181
• https://arxiv.org/abs/2303.15827