Learning Dissipative Dynamics in Chaotic Systems (Datasets)

<p>We present the datasets for NeurIPS 2022 paper <a href="https://arxiv.org/abs/2106.06898">"Learning Dissipative Dynamics in Chaotic Systems."</a> 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.</p> <p>In our work, we present results in the finite-dimensional toy system Lorenz-63. We showcase results on the 1D Kuramoto&ndash;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).</p> <p>The data is stored as .npy and .mat&nbsp;files:</p> <ul> <li><strong>L63.mat:&nbsp;</strong>Lorenz-63 data (one long trajectory of 10000 seconds)</li> <li><strong>KS.mat:</strong>&nbsp;1D Kuramoto&ndash;Sivashinsky data (1200 trajectories, 500 time-steps each)</li> <li><strong>2D_NS_Re40.npy: </strong>2D Navier-Stokes data (200 trajectories, 500 time-steps each) at 64 x 64&nbsp;spatial resolution.</li> <li><strong>2D_NS_Re500.npy: </strong>2D Navier-Stokes data (1000 trajectories, 500 time-steps each) at 64 x 64 spatial resolution with Reynolds number 500.</li> <li><strong>2D_NS_Re5000.npy: </strong>2D Navier-Stokes data (100 trajectories, 500 time-steps each) at 128 x 128 spatial resolution with Reynolds number 5000.</li> </ul>