ADE-Solver: Observation-Anchored Disentangled Evolution for Spatiotemporal PDE Solving

Spatiotemporal partial differential equation (PDE) solving is fundamental to the efficient modeling of dynamic systems whose states evolve across space and time. However, many existing methods reconstruct complete target fields from latent representations without explicitly retaining spatial structures present in the observations, requiring the model to recover existing information while learning its future changes. Moreover, different evolution effects often coexist but are typically modeled jointly, making their distinct roles difficult to identify and characterize for target state construction. To address these challenges, we propose ADE-Solver, an observation-anchored spatiotemporal PDE solver that retains the latest observation as a shared physical anchor and models future evolution through spatial transfer and state variation. Specifically, we expose changes between adjacent observations to provide explicit evolution cues, then learn distinct representations of spatial transfer and state variation from the observed dynamics, and apply them to the anchor to generate all target states in parallel. Experiments on simulated and real-world spatiotemporal PDE benchmarks demonstrate that ADE-Solver achieves average improvements of 33.81% in RMSE and 33.06% in relative $L_2$ error over the strongest baselines. The code is available at https://anonymous.4open.science/r/ADE-Solver.