Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems
Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonlinear parametrizations, such as typical neural networks or mixture models. We propose to add inertia to the Dirac-Frenkel dynamics and show that this allows useful parameter velocity information to persist from the past trajectory in directions that are weakly informed, while well-informed parameter velocity directions continue to follow the Dirac-Frenkel dynamics. We prove that the inertial formulation yields well-posed parameter dynamics and provide a posteriori error bounds. After time discretization, the meth...
| Authors | Matteo Raviola, Benjamin Peherstorfer |
|---|---|
| Primary category | math.NA |
| Published | 23 June 2026 |
| Last updated at source | 7 August 2026 |
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