Markovian Dynamics Enforcer: Feasibility Preserving Correction on Learned Dynamics Manifolds

2026-09-30

AI Summary

This study addresses the problem of neural trajectory predictors violating physical constraints when control inputs are unobserved, and proposes MaDE, a post-processing operator that projects state transitions onto a feasible manifold. By inferring unknown controls and rectifying inequality constraints, MaDE ensures dynamical consistency. Its key innovations include training without ground-truth control signals, guaranteeing iteratively optimal feasibility via gradient-based correction, and serving as a plug-and-play module for arbitrary prediction models. Experiments demonstrate that MaDE drives dynamical residuals to near zero in simulation and reduces them to 0.0071 on real-world vehicle data, outperforming baselines. This strict physical compliance is achieved at the cost of only an approximately 1.8-fold increase in displacement error.

Abstract

Neural trajectory predictors can reach low prediction error while violating dynamics, actuator limits, or state constraints, especially when controls are unobserved and dynamics are partially specified. We introduce the Markovian Dynamics Enforcer (MaDE), a time-invariant post-hoc operator mapping state-transition proposals onto a learned feasible dynamics manifold, trained on feasible states without ground-truth controls. For each transition it infers a control and recomputes the state through a completion model of known physics plus a learned residual. It then corrects that control by gradient-based inequality reduction, so inequality satisfaction is best-effort within an iteration budget. Since every correction iterate re-enters the completion model, the returned state is dynamically consistent by construction relative to that model and the supplied previous-state anchor. MaDE drives dynamics residuals to essentially zero on fully specified simulated systems, and on an underspecified system leaves a smaller true-dynamics residual than the baselines. Designed to attach to arbitrary predictors, the frozen operator is evaluated downstream of recurrent, structured state-space, and transformer predictors. On recorded vehicle trajectories the one-step residual against a kinematic bicycle model is 0.0071 to 0.0072 for MaDE and 0.1703 to 0.1714 for raw predictors. MaDE raises average displacement error by a factor of 1.57 to 1.83.

Problem

• trajectory prediction
• dynamics constraints
• feasibility
• neural predictors
• partially specified dynamics

Innovation

• Markovian Dynamics Enforcer
• Feasibility Preserving
• Dynamics Manifold
• Physics-Informed Completion
• Post-hoc Correction