Data-driven linear analysis of dynamical systems via nonlinearity-subtracted dynamic mode decomposition
arXiv:2608.13373
2026
Architecture
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper introduces nonlinearity-subtracted DMD (NSDMD) for systems of the form \(\dot{x}=Ax+f(x)\), where the nonlinear contribution \(f\) is available from physics or a simulator but the linear operator \(A\) is unknown. NSDMD subtracts measured nonlinear snapshots from time-derivative data and regresses only the residual onto state snapshots, yielding a low-rank approximation of the underlying linear operator. The strongest neural-network transfer is a gray-box latent neural ODE or state-space model that explicitly removes a known nonlinear block before learning a compact, spectrally analyzable linear backbone.
Ideas from this paper
✓✓ Beats tuned baseline
2026
Build a latent continuous-time neural model with dynamics \(\dot{z}=Az+f_\phi(z)\), where \(f_\phi\) is known, separately computed, or frozen, and \(A\) is learned exclusively from the derivative residual after subtracting \(f_\phi(z)\). Parameterize \(A\) with a truncated SVD or low-rank factorization so its eigenvalues directly predict local stability and long-horizon growth.
Useful8/10
Difficulty5/10
Novelty7/10