Colliding Thermals Dataset for Spatiotemporal SciML

This dataset contains two-dimensional colliding thermal-bubble simulations used in the MATEY study, MATEY: Multiscale Adaptive Foundation Models for Spatiotemporal Physical Systems. The dataset consists of time-history trajectories of two buoyant thermals: a cold thermal initialized near the top of the domain and a warm thermal initialized near the bottom. The two thermals evolve and collide, producing multiscale temperature, density, and velocity structures suitable for testing spatiotemporal forecasting, surrogate modeling, adaptive tokenization, and transfer learning for physical systems. The governing equations and MiniWeather formulation are referenced in the MATEY paper through Norman’s MiniWeather work. The initial temperature field is constructed as a 300 K background plus one hot and one cold localized thermal perturbation. Each thermal is elliptical, with randomly sampled center locations and shape parameters. Thermal center locations are sampled from uniform distributions over prescribed spatial ranges, the ellipse radii in the horizontal and vertical directions are sampled uniformly, and the thermal amplitudes are sampled from the set {10, 15, 20, 25}. The full dataset used in the paper contains 4,096 trajectories. Due to storage-space limitations, this release provides 23 of the 4,096 trajectories used in the arXiv paper. The simulations are solved using a finite-volume method on a 256 × 256 grid in the horizontal and vertical directions. Each simulation is advanced for 500 seconds, with solution snapshots saved every 0.5 seconds, resulting in 1,001 time snapshots per trajectory. So each trajectory corresponds to spatiotemporal resolution (nt = 1001, nx = 256, ny = 256). The MATEY CollisionDataset class identifies this dataset as thermalcollision2d and uses four model-facing state variables: density, potential temperature, horizontal velocity, and vertical velocity. The dataset class specifies the field names as dens, potentialtemperature, uwnd, and wwnd, with spatial size [256, 256]. In the original NetCDF files used by the MATEY loader, the perturbation variables dens and theta are combined with the hydrostatic background profiles hy_dens and hy_theta to reconstruct full density and full potential temperature. The model-facing tensor is then assembled as [rho_full, theta_full, uvel, wvel] and transposed to the (time, channel, height, width) layout used by MATEY. The dataset was used in MATEY for evaluating spatiotemporal attention schemes, adaptive tokenization, and fine-tuning from PDEBench-pretrained models. In the fine-tuning experiments, MATEY used colliding thermals as an out-of-distribution downstream task with physical variables distinct from those in the pretraining datasets. The fine-tuning task predicts future system states from a history of past states, with the MATEY experiments using a history length of 10 and a maximum lead time of 50 steps for colliding thermals. This release is intended for machine-learning research on spatiotemporal physical systems, including autoregressive prediction, operator learning, data-efficient fine-tuning, and adaptive tokenization.