Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models

The paper addresses the challenge of learning nonlinear dynamics from observations by framing it as a linear state-space identification problem. OSF is a convex method that provably competes with the best linear observer for the system, and the authors show how to distill it into an explicit linear state-space model. This avoids the local minima and scalability issues typical of non-convex system identification. The results have potential implications for control, time-series modeling, and model-based reinforcement learning, though further research is needed to assess practical performance on large-scale benchmarks.