Learning from Generated Contexts: Adaptive Stagewise Training for Long-horizon Forecasting

Long-horizon forecasts of physical and dynamical systems accumulate errors as generated inputs evolve during recursive deployment. We study stagewise training: successive predictors learn true futures from contexts generated by frozen predecessors. We analyze specialization gains and error propagation; population bounds motivate monitoring without prescribing individual error curves. We introduce public-boundary adaptation and sample-specific adaptation, distinguishing model training from inference-time routing. Public adaptation uses aggregate error signals to allocate a compact model chain. Sample-specific training aligns successor windows with individual slope-based handovers; inference policies are then compared on the same frozen chain. On the tokamak benchmark, public slope control uses 30–40% fewer models than a ten-model baseline, with mean-error changes from −3.35% to +2.82%. On engine and chemical benchmarks, model savings can accompany substantial accuracy losses. A diagnostic that switches when the adjacent successor reduces true scaled root mean squared error (sRMSE) by at least five percent improves mean error and q90/q95 at forecast lead 500 over learned routing on this benchmark, but requires future targets and is not uniformly best across all baselines. Learned error predictors fail to recover these gains. Across three datasets and three backbones, generated-context training reduces step-500 mean sRMSE by 17.63%–96.24% in 27 matched comparisons. Reliable individual routing remains unresolved.