arXiv:2606.10596v1 Announce Type: new 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. Exten
This research provides a theoretical foundation for embedding complex hybrid systems into continuous latent spaces, which is crucial for advancing AI's ability to model and optimize real-world dynamics.
A strategic reader should care because this breakthrough enables the application of differentiable optimization to previously intractable discontinuous systems, potentially unlocking new capabilities in control, robotics, and agentic AI.
The ability to represent intrinsically discontinuous hybrid systems as continuous vector fields changes how AI can model and interact with complex physical and cyber-physical systems.
- · AI researchers
- · Robotics engineers
- · Control systems developers
- · Defense contractors
- · Traditional modeling approaches for hybrid systems
- · Sectors reliant on non-differentiable system optimization
This work directly enables more robust and optimizable AI models for systems with discrete and continuous dynamics.
Improved modeling of hybrid systems could accelerate advancements in autonomous agents, complex industrial control, and humanoid robotics.
The enhanced ability to optimize complex systems might lead to novel designs for physical infrastructure and manufacturing processes.
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