StrataTok: Local-Variation-Guided Dynamic Tokenization for PDE Forecasting from Sparse and Irregular Observations

Observations of physical systems are often sparse and irregularly distributed across space and time. Forecasting PDE dynamics from such observations requires compact spatiotemporal tokens, but fixed tokenizers use the same predefined partition for every input, even when observation locations and locally active regions change. Existing dynamic tokenizers address this rigidity, but under sparse and irregular sampling, soft slicing leaves local variation implicit while patch-based refinement estimates it from unevenly populated or empty patches. To address this limitation, we present STRATATOK, a variation-stratified dynamic tokenizer that organizes token formation through local-variation-guided pathway allocation and learned soft slot assignment. STRATATOK first divides each observation between global and variation-enriched pathways, then forms mass-normalized tokens within each pathway. The resulting assignments admit a mass-conserving discrete transport interpretation. The two pathways form complementary token banks for global and localized dynamics. Across nine simulated PDE settings and four RealPDEBench systems, STRATATOK achieves the lowest RMSE in all thirteen comparisons among six tokenizers. The advantage persists across nearly all tested observation densities and sampling patterns, and STRATATOK ranks first at both full and halved token budgets in all four settings.