Embedding Hybrid Systems into Continuous Latent Vector Fields

Abstract:This work proves that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever $m>2n$. This result suggests that an intrinsically discontinuous hybrid system generically admits a continuous extrinsic representation that is well-posed for differentiable optimization. Building on this existence theorem, we show that a latent Neural ODE with consistency loss in both the latent and state space can accurately recover the flow of hybrid systems. Extensive experiments suggest the proposed method outperforms the existing method in learning hybrid systems with varying geometries from only time series data.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Systems and Control (eess.SY)

arXiv:2606.10596 [cs.LG]

(or arXiv:2606.10596v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.10596 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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