KMF: Physics-Guided Inference-Time Debiasing for Off-Cadence PDE Foundation Models

Scientific workflows require PDE states on temporal grids chosen by downstream analysis, often at a finer resolution than the cadence of available foundation-model outputs or observations. Direct off-cadence model queries can be biased, while standard temporal upsampling ignores the governing dynamics. We introduce Kinematic Manifold Fusion (KMF), a parameter-update-free, physics-guided inference-time correction framework for temporal refinement and autoregressive rollout. When neighboring model snapshots are available, KMF evaluates a cheap spatial PDE operator at those snapshots, constructs a local cubic Hermite physical candidate, and fuses it with a model estimate through a calibration-selected scalar. During rollout, it reuses the same local physics as a causal defect signal before reinjecting the corrected state into the frozen model. It also enforces known constraints through the corresponding exact projection when available. KMF changes no model parameters and uses zero temporal integration substeps, only instantaneous spatial right-hand-side evaluations. Under standard smoothness and operator-error assumptions, we establish a local error bound for the physical bridge and an endpoint-perturbation bound for deployment. Empirical evaluation across PDE systems, temporal cadences, and frozen foundation-model architectures demonstrates accurate temporal refinement and active causal correction in the regimes where local physics is informative, while retaining the efficiency of the underlying model. KMF offers a lightweight complement to learned continuous-time solvers and numerical integration.