arXiv：cs.LG（机器学习，全量分类）· Kevin Yu, Tao Guo, Constantinos Antoniou, Panagiotis Angeloudis·· 18 小时前AI 评分43
MaDE：在学到的动力学流形上保持可行性的马尔可夫动力学校正器
Markovian Dynamics Enforcer: Feasibility Preserving Correction on Learned Dynamics Manifolds
AI 导读
研究者提出 Markovian Dynamics Enforcer（MaDE），一种时间不变的事后算子，将状态转移提议映射到学到的可行动力学流形上，无需真实控制信号即可训练。
正文
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.
| Comments: | 26 pages, 2 figures, 11 tables. Accepted at NeurIPS 2026. Code available at this https URL |
| Subjects: | Machine Learning (cs.LG); Robotics (cs.RO); Systems and Control (eess.SY) |
| Cite as: | arXiv:2609.39888 [cs.LG] |
| (or arXiv:2609.39888v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.39888 arXiv-issued DOI via DataCite |
Submission history
From: Kevin Yu [view email]
[v1]
Wed, 30 Sep 2026 14:57:24 UTC (116 KB)
[v2]
Thu, 1 Oct 2026 12:25:50 UTC (73 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org