Title: CHyLL: Learning Continuous Neural Representations of Hybrid Systems
Primary area: learning on time series and dynamical systems
Keywords: Hybrid Systems, Topology, Geometry, Neural ODE

Abstract: 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.

TL;DR: We learn discontinuous flow in continuous space with gurantees.