🤖 AI Summary
This study addresses the challenge of learning extreme events in chaotic systems from short trajectories, which is hindered by transient instabilities. To overcome this, we propose a mechanism-aware conditioning framework that leverages ensemble covariance as an actionable conditioning signal to capture the geometric structure of local destabilization. This signal is injected into Transformer and STORN backbone networks via Feature-wise Linear Modulation (FiLM) modules, enabling Jacobian-free and non-intrusive surrogate modeling. We demonstrate the efficacy of our approach on a quasi-geostrophic flow task, where it significantly improves the statistical characterization of rare events using only limited data. Notably, the proposed method outperforms baseline models trained with ten times higher-resolution data, highlighting its potential for efficient and accurate prediction of extreme events in complex dynamical systems.
📝 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.