DAW: Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems

• URL: http://arxiv.org/abs/2608.22277v2
• Date: Wed, 26 Aug 2026 06:22:52 GMT
• Title: DAW: Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems
• Abstract summary: We introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework.<n>On the chaotic KS equation, DAW consistently outperforms uniform training, purely statistical density weighting, and its randomly permuted ablation.
• Score: 7.490065985639902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts. This behavior is partly tied to the underlying systems: chaotic spatiotemporal systems, such as the Kuramoto-Sivashinsky (KS) equation, visit phase space unevenly - dominated by recurrent, low-dimensional quiescent states (e.g., near-laminar flows) and punctuated by rare, dynamically complex topological transitions (e.g., wave-merging events). Under a sample-wise uniform objective, standard neural surrogates allocate their finite capacity to the statistically numerous quiescent states, under-representing the transient regimes that trigger disproportionate, localized errors. Existing imbalanced-regression methods reweight samples by target-space density. However, statistical target-space rarity need not coincide with the intrinsic dynamical rarity - the recurrence geometry of the attractor that is the source of the imbalance. To address this, we introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework. Using the local dimension $d$ from dynamical systems theory as an a priori measure of a state's active degrees of freedom, DAW reshapes the loss landscape to allocate representational capacity toward the sparse, high-$d$ regimes where forecast errors are systematically large. On the chaotic KS equation, DAW consistently outperforms uniform training, purely statistical density weighting, and its randomly permuted ablation, reducing long-term autoregressive error relative to all baselines. Event-level analysis shows that DAW achieves this by suppressing the localized error amplifications incurred during sharp jumps in $d$, which accompany complex physical processes such as wave-merging in the KS system.

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