Embedding Hybrid Systems into Continuous Latent Vector Fields

The paper demonstrates that an $n$-dimensional hybrid system can be embedded into an $m$-dimensional Euclidean space with a continuous vector field when $m > 2n$, enabling a continuous extrinsic representation suitable for differentiable optimization. It introduces a latent Neural ODE framework with a consistency loss that effectively recovers the flow of hybrid systems, outperforming existing methods in learning hybrid systems with diverse geometries from time series data. This work is significant for practitioners as it provides a robust approach for modeling complex hybrid systems, enhancing the capabilities of AI systems in handling discontinuous dynamics.