Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events
cs.LG, math.DS, physics.ao-ph
Submitted: 2026-09-25
Updated: 2026-09-25
Comments: Accepted to NeurIPS 2026 (oral)
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
Terminology
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.
Sources
- Fourier Neural Operator for Parametric Partial Differential Equations
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning
- P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics
- Training neural operators to preserve invariant measures of chaotic attractors
- True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics
- A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data
- Statistics of extreme events in coarse-scale climate simulations via machine learning correction operators trained on nudged datasets
- FiLM: Visual Reasoning with a General Conditioning Layer
Related papers
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
- AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
- Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
- Convergence issues in Relational Concept Analysis based on AOC-posets
- Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
- Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks