arXiv:2608.02842 2026 Dynamics 1 ideas extracted · analyzed Aug 31, 2026
The paper provides a transferable energy-dependent damping mechanism: the velocity damping coefficient grows as a power of the current fractional energy plus kinetic energy. Its key certificate is a monotone energy law in which damping produces nonnegative dissipation, while the long-time dynamics are constrained by a gradient-like flow. A direct neural-network adaptation is an inertial optimizer whose friction increases during high-energy or high-velocity excursions instead of remaining constant. The first experiment should test the predicted energy-decay relation and the location of the oscillation or divergence boundary, not only final accuracy.
Replace constant friction in a second-order neural-network optimizer by a scalar damping coefficient that grows as a power of the current parameter energy plus velocity energy. This should selectively damp large oscillations and unstable excursions while preserving lower friction during small, potentially useful movements.