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SUMMARY:Anderson-Pulay Acceleration: Convergence of Adaptive Algorithms an
 d Applications to Quantum Chemistry
DTSTART:20231017T161500
DTEND:20231017T171500
DTSTAMP:20260505T021319Z
UID:a96441ae4a75c9839870082013d3d816d4eb3968fbcdda220c8708fc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mi-Song Dupuy (Sorbonne Université)\nIn this talk\, a general
  class of non-gradient algorithms for\nsolving fixed-point problems\, name
 d Anderson-Pulay acceleration\, is\nintroduced. This family brings togethe
 r the DIIS technique (Pulay\, 1980)\nto accelerate the convergence of self
 -consistent field procedures in\nquantum chemistry\, as well as the Anders
 on acceleration (Anderson 1960)\,\nand their variations. Such methods aim 
 at accelerating the convergence\nof fixed-point problems by combining at e
 ach step several of the\nsuccessive approximations to generate the next on
 e. This process of\nextrapolation is characterized by its depth\, i.e. the
  number of previous\napproximations stored. While this parameter is decisi
 ve in the\nefficiency of the method\, in practice\, the depth is fixed wit
 hout any\nguarantee of convergence. In this presentation\, we consider two
 \nmechanisms to vary the depth during the course of the method. A first\nw
 ay is to let the depth grow until the rejection of all the stored\napproxi
 mations (except the last one) and restart the method. Another way\nis to a
 dapt the depth by eliminating some less relevant approximations\nat each s
 tep. In a general framework and under natural assumptions\, the\nlocal con
 vergence and acceleration of Anderson-Pulay acceleration\nmethods can be p
 roved. These algorithms are tested for the numerical\nresolution of the Ha
 rtree-Fock equations and the DFT Kohn-Sham model.\nThese numerical experim
 ents show a faster convergence and lower\ncomputational costs compared to 
 the traditional fixed window approach.\nThis is a joint work with Maxime C
 hupin\, Guillaume Legendre and Éric Séré.\n 
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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