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原文摘要

Dynamical systems reconstruction (DSR) aims to learn surrogate models that capture the dynamics underlying time-series data. Reliable scientific inference with these surrogates requires uncertainty estimates consistent with the learned dynamics. We expose a dynamic-probabilistic consistency (DPC) gap: optimizing finite-horizon probabilistic objectives can degrade the learned dynamics or decouple predictive uncertainty from the local tangent dynamics it should reflect. We isolate three mechanisms behind this gap: core collapse, noise masking, and blind uncertainty. Specifically, we show that open-loop rollout objectives can penalize covariance growth driven by the dynamics, encouraging optimization shortcuts that weaken local expansion. To mitigate this gap, we propose KAFFEE (Kalman-Aware Framework For Ergodic Emulation), a differentiable extended Kalman filter-based training framework that jointly learns dynamics and noise covariances by coupling filtered innovation likelihoods with covariance propagation through learned local Jacobians, while differentiating through the Kalman updates. On stochastic hyperchaotic Lorenz-96, KAFFEE mitigates the identified failure modes and improves both reconstruction of dynamical invariants and predictive scores relative to open-loop objectives. The DPC gap also appears when probabilistically adapting a DSR foundation model across 13 chaotic systems, where KAFFEE improves predictive likelihood over open-loop adaptation while preserving the pretrained model's long-term dynamics and enabling in-context Bayesian filtering.