Regularized dynamical parametric approximation for stiff evolution problems (Jörg Nick)

18.11.2025 14:00 – 15:00

Parametric approaches numerically approximate the solution of evolution equations by nonlinear parametrizations  u(t) = \Phi( q (t)) with time-dependent parameters q(t), which are to be determined in the computation.  The talk discusses numerical integrators for the resulting evolution problems for the evolving parameters q(t). The primary focus is on tackling the challenges posed by the combination of stiff evolution problems and irregular parametrizations, which typically arise with neural networks, tensor networks, flocks of evolving Gaussians, and in further cases of overparametrization. Regularized parametric versions of classical time stepping schemes for the time integration of the parameters in nonlinear approximations to evolutionary partial differential equations are presented. At each time step, an ill-conditioned nonlinear optimization problem is solved approximately with a few regularized Gauß--Newton iterations. Error bounds for the resulting parametric integrator are shown. Numerical experiments that are designed to show key properties of the proposed parametric integrators are discussed

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre