Lorenz-96

KAFFEE: Addressing the Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling

This paper identifies a 'dynamic-probabilistic consistency (DPC) gap' in dynamical systems reconstruction (DSR), where optimizing finite-horizon probabilistic objectives can degrade learned dynamics or decouple predictive uncertainty from local tangent dynamics. Three failure mechanisms are isolated: core collapse, noise masking, and blind uncertainty. The authors propose KAFFEE, a differentiable extended Kalman filter-based training framework that evaluates likelihood on local predictive residuals while transporting covariance through learned Jacobians, reducing these failure modes on stochastic hyperchaotic Lorenz-96 and across 13 chaotic systems when adapting a DSR foundation model.