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The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: State-space inference for stochastic systems · 0 citations (OpenAlex)

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Identifies a dynamic-probabilistic consistency gap in probabilistic dynamical systems reconstruction and proposes KAFFEE, a differentiable EKF training framework that scores filtered innovations with Jacobian-based covariance transport, tested on stochastic Lorenz-96 and DynaMix adaptation.

Problem

Probabilistic training of chaotic dynamical-systems surrogates with finite-horizon Gaussian objectives can degrade autonomous dynamics or decouple predictive uncertainty from local Jacobian dynamics.

Approach

Evaluate the likelihood on EKF innovations (filtered local residuals) while transporting covariance through learned local Jacobians, instead of scoring long open-loop Gaussian rollout covariances whose volume penalizes chaotic expansion.

Key results

• On stochastic Lorenz-96, KAFFEE (tied transport, filtered) achieves NLL 1.535 and CRPS 0.632 versus 2.197 and 1.642 for open-loop tied transport, with G_tan 0.475 vs 0.180.
• Open-loop objectives collapse hyperchaotic expansion (|Delta h_lambda^core| about 4.8) whereas KAFFEE reaches 0.999 and the filtered no-transport variant reaches 0.421.
• On 13 DynaMix target systems, KAFFEE matches or improves held-out NLL of open-loop fine-tuning while drifting less from the pretrained attractor.

Surprising findings

• Filtered no-transport covariance achieves the best core Lyapunov-exponent reconstruction (|Delta h| 0.421) yet shows near-zero G_tan, i.e., blind uncertainty.
• Local NLL and CRPS are tightly clustered among filtered objectives, so calibration metrics alone cannot separate dynamically grounded uncertainty from blind uncertainty.

Limitations

• EKF Gaussian local approximation may not capture multimodal or heavy-tailed uncertainty in chaotic regimes.
• EKF cost is cubic in the number of latents, limiting high-dimensional application.
• DynaMix adaptation evaluated with only 10 optimization steps and a diagonal covariance shell.

Experimental setup

Datasets: stochastic Lorenz-96 13 held-out chaotic systems

Benchmarks: stochastic Lorenz-96 (N=20, F=8) 13 held-out chaotic systems with 10% observation noise

Metrics: NLL CRPS G_tan (Spearman rank correlation of log expansion factors) D_stsp Lyapunov exponent error |Delta h_lambda| Hellinger distance

Baselines: open-loop Gaussian NLL (tied transport) no-transport covariance frozen-core shell calibration AL-RNN deterministic prior noise-only shell adaptation

Builds on: extended Kalman filter almost-linear RNN generalized teacher forcing DynaMix

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