Dynamical systems reconstruction (DSR) aims to learn surrogate models that capture the dynamics underlying time-series data. Reliably deploying these surrogates requires uncertainty estimates consistent with the learned dynamics. We expose a dynamic-probabilistic consistency (DPC) gap: the pursuit of finite-horizon probabilistic objectives can degrade dynamics or decouple predictive uncertainty from the local tangent dynamics it ought to reflect. We isolate three mechanisms behind this gap: core collapse, noise masking, and blind uncertainty. Specifically, we show that open-loop Gaussian rollout objectives can penalize Jacobian-generated covariance growth in chaotic systems, encouraging optimization shortcuts that weaken physical expansion or decouple uncertainty from it. To mitigate this gap, we propose KAFFEE (Kalman-Aware Framework For Ergodic Emulation), a differentiable extended Kalman filter-based training framework that evaluates likelihood on local predictive residuals (innovations) while transporting covariance through learned local Jacobians. On stochastic hyperchaotic Lorenz-96, KAFFEE reduces the identified failure modes, improves reconstruction of dynamical invariants relative to open-loop objectives, and maintains competitive predictive scores. We further show that the DPC gap appears when probabilistically adapting a DSR foundation model across 13 chaotic systems, where KAFFEE enables in-context Bayesian filtering while largely preserving zero-shot dynamics.

翻译：动力学系统重构旨在学习能够捕捉时间序列数据背后动力学的替代模型。可靠部署这些替代模型需要与所学动力学一致的不确定性估计。我们揭示了一个动态-概率一致性差距：追求有限时域概率目标可能退化动力学特性，或使预测不确定性脱离其本应反映的局部切向动力学。我们分离了导致这一差距的三种机制：核心坍缩、噪声掩蔽和盲目不确定性。具体而言，我们证明开环高斯展开目标会惩罚混沌系统中雅可比矩阵生成的协方差增长，从而鼓励削弱物理扩张或使其与不确定性解耦的优化捷径。为缓解该差距，我们提出KAFFEE（基于卡尔曼感知的遍历仿真框架），这是一个可微扩展卡尔曼滤波训练框架，在通过所学局部雅可比矩阵传递协方差的同时，基于局部预测残差（创新量）评估似然。在随机超混沌Lorenz-96系统上，KAFFEE减少了已识别的失效模式，相较于开环目标改善了动力学不变量的重构，并保持了具有竞争力的预测分数。我们进一步证明，当以概率方式将动力学系统重构基础模型应用于13个混沌系统时会出现动态-概率一致性差距，而KAFFEE在基本保持零样本动力学特性的同时，实现了上下文贝叶斯滤波。