Controlling Transient Amplification Improves Long-horizon Rollouts

• URL: http://arxiv.org/abs/2605.08856v2
• Date: Fri, 15 May 2026 09:57:10 GMT
• Title: Controlling Transient Amplification Improves Long-horizon Rollouts
• Abstract summary: We identify transient perturbations around rollout trajectories as a mechanism driving rollout error.<n>We propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians.<n>We show that the method improves FourNet climate forecasts on ERA5 without using any new data.
• Score: 33.85418321772749
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of perturbations around rollout trajectories as a structural mechanism driving rollout error. Using a linearization analysis we show that when the Jacobians along an autoregressive trajectory are non-normal and non-commuting, the model amplifies errors transiently, resulting in model rollout drift even when the overall system is asymptotically stable. Building on the analysis, we propose commutativity regularization: a combination of two penalties designed to reduce the normality defect of individual Jacobians and the commutator norm of Jacobians across steps. The penalties are estimated with Jacobian-vector products and have no inference-time cost. We show a propagator bound that quantifies rollout error under approximate commutativity and normality. We evaluate UNet and FNO variants with commutativity regularization on 1D and 2D spatio-temporal data in synthetic and real settings, showing successful long-horizon rollouts over thousands of steps. Further, we show that the method improves FourCastNet climate forecasts on ERA5 without using any new data. The gain is most pronounced out-of-distribution: trained on trajectories of a few hundred steps, regularized models remain in-distribution for thousands of rollout steps on initial conditions where baselines diverge.

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