Second order systems on Hilbert spaces with nonlinear damping
arXiv:2607.08506
2026
Dynamics
1 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper provides a constructive maximal-monotone formulation for nonlinear second-order dynamics, with a dissipativity calculation proving that differences between trajectories cannot grow in the system energy. The transferable asset is the combination of implicit nonlinear damping, passivity variables, and contraction-semigroup reasoning, rather than the infinite-dimensional setting itself. This can be used to build stable second-order recurrent or state-space neural blocks whose damping remains nonexpansive even when it is nonsmooth or strongly nonlinear.
Ideas from this paper
✗ Failed on benchmark
2026
Replace an unconstrained second-order residual or state-space block with a position-velocity system whose damping is the gradient or subgradient of a convex function. Compute the next state implicitly, so the damping cannot inject energy and the resulting layer is robust to large learned damping nonlinearities, nonsmooth activations, and long rollouts.
Useful7/10
Difficulty5/10
Novelty5/10