Align the Skip: Spatially Aligned and Temporally Resolved Hierarchical Surrogates for Multiscale Turbulence

Hierarchical encoder-decoder surrogates efficiently represent multiscale turbulent dynamics, but their skip connections fuse input-time encoder features with future-oriented decoder features at matching grid indices. Under advection, these features need not remain spatially correspondent. We introduce decoder-predicted spatial alignment, which learns where encoder features should be sampled before skip fusion. Across three fluid and plasma benchmarks, alignment substantially improves autoregressive forecasting and supports accurate prediction of multiple states within a larger forecast interval, reducing complete autoregressive model calls while preserving intermediate-time outputs. These intermediate states also partition each outer interval into shorter subintervals for physics-informed training through equation supervision. At a fixed outer interval, increasing the number of internal subintervals from one to eight reduces the 64-step Kolmogorov-flow relative error by more than 40%, bringing equation-supervised performance close to data-supervised accuracy without using future-state targets. We further train full-resolution surrogates using spatially reduced observations of the training initial states together with a persistent prediction-derived unresolved state. This state is iteratively constructed from model predictions and carried across optimization, allowing initially absent fine-scale structure to emerge and adapt. Reducing the effective training observations from 64x64 to only 2x2 block averages, a 1024x reduction in observed spatial values, increases the 64-step error by just 17% when evaluation begins from full-resolution held-out states. Even when the observed training states contain no spatial variation, small white noise seeds unresolved structure that is subsequently developed through equation supervision and persistent model-generated state. These results show that explicit spatial correspondence and temporally resolved equation supervision improve multiscale forecasting while reducing reliance on paired current-to-future states and spatially resolved training initial conditions.