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SUMMARY:Robust time integration for dynamical low-rank approximation
DTSTART:20220307T161500
DTEND:20220307T180000
DTSTAMP:20260408T035031Z
UID:3310e6c44c73c97af4b1a3e28a44d7b3dab530d66948a60317511807
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Christian Lubich (University of Tuebingen)\nThe talk beg
 ins with a brief review of dynamical low-rank approximation for matrix (an
 d tensor) differential equations\, emphasizing the difficulties created by
  the ubiquitous  appearance of small singular values. These difficulties 
 are overcome by the projector-splitting integrator\, which splits the proj
 ection onto the tangent space of the low-rank manifold into an alternating
  sum of subprojections. It has a surprising exactness property and is robu
 st to small singular values. A very recent robust integrator is the ``unco
 nventional'' low-rank integrator\, which uses a basis-update and Galerkin 
 approach. It shares the robust error bounds with the projector-splitting i
 ntegrator but is more parallel and avoids the backward substep that appear
 s problematic for strongly dissipative problems. Augmenting the Galerkin s
 tep to the larger subspace generated by both the old and new bases and usi
 ng a tolerance-controlled rank truncation after the step yields a novel ra
 nk-adaptive integrator with remarkable (near-)conservation properties. Num
 erical experiments illustrate the theoretical results.\nWhile the talk wil
 l be restricted to dynamical low-rank approximation for matrix differentia
 l equations in order to highlight basic construction principles\, the meth
 ods discussed here can all be nontrivially extended to robust time integra
 tion methods for general tree tensor network approximations.\n\nThis talk 
 is based on joint work with Ivan Oseledets and with Emil Kieri and Hanna W
 alach (projector-splitting integrator)\, with Gianluca Ceruti (unconventio
 nal integrator\, rank-adaptive integrator) and Jonas Kusch (rank-adaptive 
 integrator). Recent work on time integration of general tree tensor networ
 ks is jointly with Hanna Walach\, Gianluca Ceruti and Dominik Sulz.
LOCATION:CM 1 5 https://plan.epfl.ch/?room==CM%201%205
STATUS:CONFIRMED
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