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Markovian Dynamics Enforcer: Feasibility Preserving Correction on Learned Dyanmics Manifolds

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: Latent-space control and planning

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Proposes MaDE, a frozen post-hoc one-step operator that infers controls from state transitions and recomputes states through a known-physics-plus-residual model, then corrects inequality violations by control-space gradient descent.

Problem

Neural trajectory predictors can have low error yet violate dynamics, actuator limits, or state constraints when controls are unobserved and physics is only partially specified.

Approach

A time-invariant Markovian correction cell composes an inverse-dynamics model, an APHYNITY-style completion model (known physics plus minimum-norm learned residual), and a control-space inequality corrector that re-integrates the state at every iterate, so returned states are dynamically consistent with the learned model by construction.

Key results

• On the inD recordings, MaDE's one-step residual against the 2.7 m kinematic bicycle is 0.00712 to 0.00722 versus 0.1703 to 0.1714 for raw predictors.
• MaDE raises ADE by a factor of 1.57 to 1.83 over raw predictors on inD (accuracy cost).
• On the simulated DI, UNI and KB systems MaDE drives Dyn.-K below 0.0004 and has the lowest fidelity error on all four systems (e.g., DB fidelity 5.20 vs 12.51 for FAB).

Surprising findings

• Completion alone (without the corrector) raises inequality violation rate above the raw forecast in all 45 cells (0.1178 vs 0.0504), with the corrector bringing it below raw.
• MaDE has the highest FDE of the compared methods in every predictor family, so the dynamics consistency comes at a notable accuracy cost.

Limitations

• Inequality satisfaction is best-effort within a fixed iteration budget; corrector reaches the 50-iteration cap with violation above tolerance on 0.964% of calls.
• Dynamics consistency is model-relative and does not guarantee agreement with the true system; on inD MaDE's ADE rises 1.57-1.83x.
• Recursive application can propagate infeasible anchors; scope limited to one-step locality and state sufficiency.

Experimental setup

Datasets: inD simulated double integrator simulated unicycle simulated kinematic bicycle simulated dynamic bicycle

Benchmarks: inD simulated four-system ladder (DI, UNI, KB, DB)

Metrics: Ineq. rate Ineq. mag. Dyn.-K Dyn.-L Dyn.-T Fid. ADE FDE

Baselines: Clamp-only per-step MLP FAB EKF/RTS smoother raw predictor

Builds on: DC3 APHYNITY Fast Autoencoder-Based Projections

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