Markovian Dynamics Enforcer: Feasibility Preserving Correction on Learned Dyanmics Manifolds

Neural trajectory predictors are increasingly used in physical-system pipelines for reconstruction, simulation, forecasting, and downstream analysis. In these settings, low prediction error alone is insufficient. A trajectory may remain statistically plausible while violating dynamics, actuator limits, or state constraints, making it unreliable for physical interpretation or control-aware reasoning. This problem is especially difficult when controls are unobserved and the available dynamics model is only partially specified. We introduce the Markovian Dynamics Enforcer (MaDE), a framework for post-hoc feasibility enforcement under learned controlled dynamics. MaDE acts as a time-invariant correction operator that maps state-transition proposals onto a learned feasible dynamics manifold. For each transition, it infers latent controls through inverse dynamics, recomputes state evolution using a known-physics model augmented with a learned residual, and corrects controls through gradient-based inequality reduction while re-integrating the dynamics after each correction step. MaDE is trained from feasible state observations without ground-truth controls and is designed to operate as a frozen downstream layer for arbitrary trajectory predictors. We evaluate MaDE on simulated controlled systems spanning fully specified and underspecified dynamics, with deterministic bound-violation and Gaussian observation-noise stress tests. MaDE is the only method that drives known-, learned-, and true-dynamics residuals to essentially zero across the fully specified systems. In the underspecified dynamic-bicycle setting, it reduces true-dynamics residual from 1.40--2.90 for the baselines to 0.33, while reducing trajectory fidelity error by more than 60% relative to the next-best method. These results show that MaDE enforces model-relative physical feasibility while preserving proximity to the original trajectory.