用隐空间连续表示法，让混合系统动态预测更准确。
CHyLL: Learning Continuous Neural Representations of Hybrid Systems
- 在高维隐空间中学习无奇点的连续表示，避免分段建模。
- 无需事件函数或模式切换，仍能精确预测系统流形演化。
- 适用于控制优化与拓扑不变量识别，适合动态系统研究者。
学习兼具连续与离散时间动态的混合系统流形具有挑战性。现有方法在每个离散模式下分别学习动力学，受限于模式切换和流的不连续性。本文提出CHyLL（隐空间中的连续混合系统学习），无需轨迹分割、事件函数或模式切换，即可学习混合系统的连续神经表示。其核心思想是：重置映射将状态空间在守卫面处粘合，重构为分段光滑商流形，使流在空间上保持连续。基于微分拓扑中的嵌入定理，CHyLL同时学习高维空间中的无奇点神经嵌入及其连续流。实验表明，该方法可实现更高精度的系统流预测，并能识别混合系统的拓扑不变量。最后，我们将CHyLL应用于随机最优控制问题。
原文摘要 · Abstract (English)
Learning the flows of hybrid systems that have both continuous and discrete time dynamics is challenging. The existing method learns the dynamics in each discrete mode, which suffers from the combination of mode switching and discontinuities in the flows. In this work, we propose CHyLL (Continuous Hybrid System Learning in Latent Space), which learns a continuous neural representation of a hybrid system without trajectory segmentation, event functions, or mode switching. The key insight of CHyLL is that the reset map glues the state space at the guard surface, reformulating the state space as a piecewise smooth quotient manifold where the flow becomes spatially continuous. Building upon these insights and the embedding theorems grounded in differential topology, CHyLL concurrently learns a singularity-free neural embedding in a higher-dimensional space and the continuous flow in it. We showcase that CHyLL can accurately predict the flow of hybrid systems with superior accuracy and identify the topological invariants of the hybrid systems. Finally, we apply CHyLL to the stochastic optimal control problem.
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