Learning Dissipative Dynamics in Chaotic Systems (Datasets)

We present the datasets for NeurIPS 2022 paper "Learning Dissipative Dynamics in Chaotic Systems." In this work, we propose a machine learning framework, which we call the Markov Neural Operator (MNO), to learn the underlying solution operator for dissipative chaotic systems, showing that the resulting learned operator accurately captures short-time trajectories and long-time statistical behavior.

In our work, we present results in the finite-dimensional toy system Lorenz-63. We showcase results on the 1D Kuramoto–Sivashinsky (KS) and on the 2D Navier-Stokes (Kolmogorov flows) PDEs. We present the datasets for Lorenz-63, KS, and Navier-Stokes (Reynolds numbers 40, 500, and 5000).

The data is stored as .npy and .mat files:

L63.mat: Lorenz-63 data (one long trajectory of 10000 seconds)

KS.mat: 1D Kuramoto–Sivashinsky data (1200 trajectories, 500 time-steps each)

2D_NS_Re40.npy: 2D Navier-Stokes data (200 trajectories, 500 time-steps each) at 64 x 64 spatial resolution.

2D_NS_Re500.npy: 2D Navier-Stokes data (1000 trajectories, 500 time-steps each) at 64 x 64 spatial resolution with Reynolds number 500.

2D_NS_Re5000.npy: 2D Navier-Stokes data (100 trajectories, 500 time-steps each) at 128 x 128 spatial resolution with Reynolds number 500.