Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events
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.
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BibTeX
@misc{thiel2026mechanismaware,
title = {{Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events}},
author = {Isabella S. Thiel and Juan Bello-Rivas and Yannis G. Kevrekidis and Themistoklis P. Sapsis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30746},
eprint = {2609.30746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30746},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events
AU - Isabella S. Thiel
AU - Juan Bello-Rivas
AU - Yannis G. Kevrekidis
AU - Themistoklis P. Sapsis
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30746
UR - https://arxiv.org/abs/2609.30746
AB - 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.
ER -