做混沌系统建模或动力学重建的研究者，KAFFEE直接解决了概率预测与动力学一致性脱节的痛点，值得在实验中尝试。
该研究揭示了混沌系统代理建模中的动态-概率一致性（DPC）差距：追求有限时域概率目标会削弱动力学重建或使预测不确定性脱离局部切向动力学。论文识别了三种机制：核心坍缩、噪声掩盖和盲不确定性。为解决此问题，提出KAFFEE框架，基于可微扩展卡尔曼滤波训练，通过局部预测残差评估似然度，同时通过学习到的局部雅可比矩阵传递协方差。在随机超混沌Lorenz-96系统上，KAFFEE减少了故障模式，改进了动力学不变量重建，并保持了竞争性预测分数。该框架在13个混沌系统上实现了上下文贝叶斯滤波，同时保留了零样本动力学。
The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling
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.