Stabilizing autoregressive forecasts in chaotic systems via multi-rate latent recurrence

Abstract: Long-horizon autoregressive forecasting of chaotic dynamical systems remains challenging due to rapid error amplification and distribution shift: small one-step inaccuracies compound into physically inconsistent rollouts and collapse of large-scale statistics. We introduce MSR-HINE, a hierarchical implicit forecaster that augments multiscale latent priors with multi-rate recurrent modules operating at distinct temporal scales. At each step, coarse-to-fine recurrent states generate latent priors, an implicit one-step predictor refines the state with multiscale latent injections, and a gated fusion with posterior latents enforces scale-consistent updates; a lightweight hidden-state correction further aligns recurrent memories with fused latents. The resulting architecture maintains long-term context on slow manifolds while preserving fast-scale variability, mitigating error accumulation in chaotic rollouts. Across two canonical benchmarks, MSR-HINE yields substantial gains over a U-Net autoregressive baseline: on Kuramoto-Sivashinsky it reduces end-horizon RMSE by 62.8% at H=400 and improves end-horizon ACC by +0.983 (from -0.155 to 0.828), extending the ACC >= 0.5 predictability horizon from 241 to 400 steps; on Lorenz-96 it reduces RMSE by 27.0% at H=100 and improves end horizon ACC by +0.402 (from 0.144 to 0.545), extending the ACC >= 0.5 horizon from 58 to 100 steps.