Koopman Spectral Analysis of Lithium-Ion Battery Dynamics: State of Charge as a Marginally Stable Observable

What the math gives to ML

The paper provides a constructive way to extract slowly varying, physically meaningful coordinates from nonlinear input-output dynamics: delay-lift measurements into a Hankel state, fit a controlled linear operator, and inspect its spectrum. The transferable asset is not battery chemistry itself, but the combination of nonparametric delay coordinates, DMD with control, and explicit preservation of marginally stable modes near eigenvalue one. This suggests initializing or constraining a neural state-space model with a data-estimated linear backbone, rather than asking gradient descent to discover long-memory modes from scratch. The most practical first test is a residual neural SSM whose transition matrix is initialized by DMDc and whose near-unit eigenmodes are retained or softly regularized.