Modified Wave Equation: When do World Models Sucessfully Learn Dynamical Systems?

About this dataset This Zenodo resource contains the modified wave equation dataset from the paper 'When do World Models Sucessfully Learn Dynamical Systems?'$^1$ . The other datasets can be found at the following links: Flow Around a Cylinder and Periodic Wake-Impacted Flow for Generative Learning$^3$: https://doi.org/10.5281/zenodo.18457565 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)$^2$ 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. $^1$ Ross et. al. (2025)$^2$ Kassam et. al. (2005)$^3$ Winhart et. al (2024-26)