马尔可夫动力学强制器：学习动力学流形上的可行性保持校正
Markovian Dynamics Enforcer: Feasibility Preserving Correction on Learned Dynamics Manifolds
- Imperial College London（帝国理工学院）
- Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
MaDE是一种时不变后处理算子，通过推断控制并校正以满足约束，将神经轨迹预测器的状态转移映射到可行动力学流形，显著降低动力学残差，但平均位移误差略有增加。
AI中文摘要：
神经轨迹预测器在违反动力学、执行器限制或状态约束的情况下可以达到较低的预测误差，尤其是在控制未被观测且动力学部分指定时。我们引入了马尔可夫动力学强制器（MaDE），一种时不变的后处理算子，将状态转移提议映射到学习到的可行动力学流形上，该算子仅在可行状态上训练，无需真实控制。对于每个转移，它推断一个控制，并通过已知物理加学习残差的补全模型重新计算状态。然后通过基于梯度的不等式缩减来校正该控制，使得不等式满足在迭代预算内尽力而为。由于每次校正迭代重新进入补全模型，返回的状态相对于该模型和提供的前一状态锚点在构造上是动力学一致的。MaDE在完全指定的模拟系统上将动力学残差驱动到基本为零，在欠指定系统上留下的真实动力学残差小于基线。设计为可附加到任意预测器，冻结算子在下游的循环、结构化状态空间和变换器预测器上进行评估。在记录的车辆轨迹上，对运动学自行车模型的一步残差，MaDE为0.0071至0.0072，原始预测器为0.1703至0.1714。MaDE将平均位移误差提高了1.57至1.83倍。
英文摘要：
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.
