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SUMMARY:Regularized dynamical parametric approximation for stiff evolution
  problems
DTSTART:20250520T161500
DTSTAMP:20260416T135340Z
UID:4912f028073a3ffffa73963107523a971ab756b9eb214e54de4a41f5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Jörg Nick\, ETH Zürich\nAbstract : Evolutionary deep neu
 ral networks have emerged as a rapidly growing field of research. This tal
 k\ndiscusses numerical integrators for such and other classes of nonlinear
  parametrizations u(t) = Φ(θ(t)) where\nthe evolving parameters θ(t) ar
 e to be computed. The primary focus is on tackling the challenges posed\nb
 y the combination of stiff evolution problems and irregular parametrizatio
 ns\, which typically arise with\nneural networks\, tensor networks\, flock
 s of evolving Gaussians\, and in further cases of overparametrization.\nRe
 gularized parametric versions of classical time stepping schemes for the t
 ime integration of the parameters\nin nonlinear approximations to evolutio
 nary partial differential equations are presented. At each time step\,\nan
  ill-conditioned nonlinear optimization problem is solved approximately wi
 th a few regularized Gauß–\nNewton iterations. Error bounds for the res
 ulting parametric integrator are shown. Numerical experiments\nthat are de
 signed to show key properties of the proposed parametric integrators are d
 iscussed.
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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