S3GM: Learning spatiotemporal dynamics with a pretrained generative model

<h1>Datasets of Kuramoto-Sivashinsky equation (KSE) and Kolmogorov flow.</h1> <h2>Description of KSE data:</h2> <p>Each file for KSE datasets contains 4 dimensions in the following order: (B*V)*T*X*C. Details are listed in the following table:</p> <table> <tbody> <tr> <td>B</td> <td>number of varying initial conditions</td> </tr> <tr> <td>V</td> <td>number of varying parameters</td> </tr> <tr> <td>T</td> <td>number of temporal frames</td> </tr> <tr> <td>X</td> <td>spatial resolution</td> </tr> <tr> <td>C</td> <td>number of variables in solution (C = 1 for KSE)</td> </tr> <tr> <td>values of parameter used to generate <strong>training </strong>dataset</td> <td>1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0</td> </tr> <tr> <td>values of parameter used to generate <strong>test </strong>dataset</td> <td>1.1, 2.5, 3.2</td> </tr> </tbody> </table> <h2>Description of Kolmogorov flow data:</h2> <p>Each file for Kolmogorov flow contains 5 dimensions inthe following order: (B*Re*K)*T*X*X*C. Details are listed in the following table:</p> <table> <tbody> <tr> <td>B</td> <td>number of varying initial conditions</td> </tr> <tr> <td>Re</td> <td>number of varying Reynolds numbers</td> </tr> <tr> <td>K</td> <td>number of varying source terms (controled by the value of k)</td> </tr> <tr> <td>T</td> <td>number of temporal frames</td> </tr> <tr> <td>X</td> <td>spatial resolution</td> </tr> <tr> <td>C</td> <td>number of variables in solution (C = 2 for Kolmogorov flow)</td> </tr> <tr> <td>values of Reynolds number used to generate <strong>training </strong>dataset</td> <td>100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050</td> </tr> <tr> <td>values of Reynolds number used to generate&nbsp;<strong>test </strong>dataset</td> <td> <div> <div>50, 125, 575, 1100, 1500</div> </div> </td> </tr> <tr> <td>values of k used to generate <strong>training </strong>dataset</td> <td>2, 3, 4, 5, 6, 7, 8</td> </tr> <tr> <td>values of k used to generate <strong>test </strong>dataset</td> <td> <div> <div>2, 4, 6, 8</div> </div> </td> </tr> </tbody> </table> <h2>Description of ERA5 data:</h2> <p>Training and testing dataset for ERA5 contains 5 dimensions inthe following order: 1*T*X*X*C, which is manually collected from <a href="https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=download">https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=download</a>. <strong>Note that the quantities in the datasets are already rescaled</strong> (the scale factors are saved in the scalar_era5.npy file, which is a 4x2 array recording the means and stds for the 4 quantities we used). Details are listed in the following table:</p> <table> <tbody> <tr> <td>T</td> <td>number of temporal frames</td> </tr> <tr> <td>X</td> <td>spatial resolution</td> </tr> <tr> <td>C</td> <td>number of variables in solution (C = 4 for ERA5)</td> </tr> <tr> <td>time span for <strong>training </strong>dataset</td> <td>1979-2022</td> </tr> <tr> <td>time span for <strong>test </strong>dataset</td> <td> <div> <div>2023</div> </div> </td> </tr> </tbody> </table> <h2>Pretrained checkpoints:</h2> <p>The .zip file contains the pretrained checkpoints for KSE, Kolmogorov flow and ERA5. Within the .zip file, the folder'kse_v0' is the checkpoint for KSE, 'kol_v0' is the checkpoint for Kolmogorov flow, and 'era5_v0' is the checkpoint for ERA5.</p> <h1><em>Source code:</em></h1> <p>The source code is upload as Github repository in <a href="https://github.com/lzy12301/S3GM">https://github.com/lzy12301/S3GM</a></p>