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This research introduces a mechanism-aware conditioning framework that leverages ensemble covariance to detect local instability geometry in chaotic systems, enabling more accurate emulation of rare extreme events with limited data. By integrating this signal via a lightweight FiLM module, the approach significantly reduces errors in tail statistics without altering the underlying coarse simulator or requiring extensive high-resolution training data. The method demonstrates that understanding transient finite-time instabilities is crucial for improving long-horizon predictions in both low-dimensional benchmarks and complex atmospheric flow models.
Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events
arXiv:2609.30746v1 Announce Type: new Abstract: Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by transient finite-time instability rather than by frequently observed bulk dynamics. We propose a mechanism-aware conditioning plug-in framework that turns a nudged coarse ensemble into a non-intrusive sensor of local instability geometry. In the small-noise regime, the ensemble covariance aggregates the same finite-time deformation kernels that govern local instability, providing a Jacobian-free proxy for the local amplification structure around a synchronized coarse trajectory. A small FiLM module injects statistics of this ensemble geometry into an otherwise unchanged backbone while leaving the coarse simulator unchanged. We demonstrate this interface in two distinct pipelines: a Transformer-style residual-attention corrector for a controlled low-dimensional chaotic system and a probabilistic recurrent STORN corrector for topographic two-layer quasi-geostrophic (QG) flow. In the low-dimensional benchmark, ensemble covariance directions co-activate with OTD modes and FiLM conditioning improves 99th-percentile exceedance-frequency errors over an identical no-context Transformer baseline. In QG, a fixed ensemble-conditioned FiLM-STORN model trained on only \(50\) time units substantially improves long-horizon rare-event statistics in the data-limited regime, including density-tail errors, exceedance frequencies, and spatial exceedance-area distributions relative to an unconditioned STORN trained on the same data; on averaged high-threshold exceedance diagnostics, it also outperforms the baseline STORN trained with $20$ times more high-resolution data. These results show that local instability geometry is not merely interpretable post hoc, but an actionable conditioning signal for data-efficient rare-event emulation.
Abstract:Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by transient finite-time instability rather than by frequently observed bulk dynamics. We propose a mechanism-aware conditioning plug-in framework that turns a nudged coarse ensemble into a non-intrusive sensor of local instability geometry. In the small-noise regime, the ensemble covariance aggregates the same finite-time deformation kernels that govern local instability, providing a Jacobian-free proxy for the local amplification structure around a synchronized coarse trajectory. A small FiLM module injects statistics of this ensemble geometry into an otherwise unchanged backbone while leaving the coarse simulator unchanged. We demonstrate this interface in two distinct pipelines: a Transformer-style residual-attention corrector for a controlled low-dimensional chaotic system and a probabilistic recurrent STORN corrector for topographic two-layer quasi-geostrophic (QG) flow. In the low-dimensional benchmark, ensemble covariance directions co-activate with OTD modes and FiLM conditioning improves 99th-percentile exceedance-frequency errors over an identical no-context Transformer baseline. In QG, a fixed ensemble-conditioned FiLM-STORN model trained on only \(50\) time units substantially improves long-horizon rare-event statistics in the data-limited regime, including density-tail errors, exceedance frequencies, and spatial exceedance-area distributions relative to an unconditioned STORN trained on the same data; on averaged high-threshold exceedance diagnostics, it also outperforms the baseline STORN trained with $20$ times more high-resolution data. These results show that local instability geometry is not merely interpretable post hoc, but an actionable conditioning signal for data-efficient rare-event emulation.
Machine Learning (cs.LG); Dynamical Systems (math.DS); Atmospheric and Oceanic Physics (physics.ao-ph)
arXiv:2609.30746 [cs.LG]
(or arXiv:2609.30746v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.30746 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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