CHyLL: Learning Continuous Neural Representations of Hybrid Systems

TMLR Paper7365 Authors

Abstract: Learning the flows of hybrid systems with both continuous and discrete 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 demonstrate that CHyLL can accurately predict the flow of hybrid systems with superior accuracy and identify their topological invariants. Finally, we apply CHyLL to the stochasticoptimal control problem.

Submission Type: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=Zb4klg5L5S

Changes Since Last Submission: Desk rejected for font change. Corrected now. Same title and content.

Assigned Action Editor: ~Arash_Mehrjou1

Submission Number: 7365