Modified 2D Heat, Wave and Kuramoto-Sivashinsky on the Torus

About this dataset Three ordinary differential equations (a modified heat and wave equation, and the Kuramoto-Sivashinsky equation) are solved with numerical solvers on a discretised torus. Parameters Parameter Heat Wave KSE Resolution 128 x 128 128 x 128 256 x 256 Timesteps 2000 2000 2000 Folder structure /heat/{operator}/{init_cond} /wave/{operator}/{init_cond} /kse/{init_cond} File structure Pytorch Pickletensor Pytorch Pickletensor Pytorch Pickletensor Numerical method Explicit Euler Explicit Euler ETDRK4 (Modified)[^1] Time factor 0.4 0.05 0.01 No. simulations 4 x 100 2 x 100 28 Further Details All datasets are 2D. A 500 frame burn-in time was discarded from the KSE simulations, to give the 2000 frame datasets shared here. The heat and wave equations use a modified Laplacian, namely $\tilde{\nabla}^2 \rightarrow \nabla^T A \nabla$ for some positive definite, stochastically generated, diagonal matrix $A$. This modified operator is provided as op.pt in the relevant folder. Each run with a given operator simulates 100 stochastically generated initial conditions for 2000 frames, hence the folder structure. [^1]: Kassam, A.-K., & Trefethen, L. N. (2005). Fourth-order time-stepping for stiff PDEs. SIAM Journal on Scientific Computing, 26(4), 1214–1233. https://doi.org/10.1137/S1064827502410633 The data was originally used to train and validate generative models. The results of these studies are presented in the article[^2] [^2]: Ross, E., Drygala, C., Schwarz, L., Kaiser, S., di Mare, F., Breiten, T., & Gottschalk, H. (2025). When do World Models Successfully Learn Dynamical Systems? arXiv. https://doi.org/10.48550/arXiv.2507.04898