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.Z. Li gratefully acknowledges the financial support from the Kortschak Scholars, PIMCO Fellows, and Amazon AI4Science Fellows programs. M. Liu-Schiaffini is supported by the Stephen Adelman Memorial Endowment. A. Anandkumar is supported in part by Bren endowed chair. K. Bhattacharya, N. B. Kovachki, B. Liu, A. M. Stuart gratefully acknowledge the financial support of the Army Research Laboratory through the Cooperative Agreement Number W911NF-12-0022. A. M. Stuart is also grateful to the US Department of Defense for support as a Vannevar Bush Faculty Fellow. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. A part of this work took place when K. Azizzadenesheli was at Purdue University. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein