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SUMMARY:John Simon (Institute of Mathematics\, Czech Academy of Sciences)
DTSTART:20221114T144000Z
DTEND:20221114T161000Z
DTSTAMP:20260405T174814Z
UID:NSCM/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NSCM/78/">A 
 NAIVE FORMULATION OF MAXIMIZING THE COMPUTATIONAL CAPABILITY OF THE TWIN V
 ORTEX COMPUTER VIA SHAPE OPTIMIZATION</a>\nby John Simon (Institute of Mat
 hematics\, Czech Academy of Sciences) as part of Nečas Seminar on Continu
 um Mechanics\n\nLecture held in Room K3\,  Faculty of Mathematics and Phys
 ics\, Charles University\, Sokolovská 83  Prague 8..\n\nAbstract\nPhysica
 l reservoir computing is a new computational paradigm based on recurrent n
 eural networks\nwhere instead of optimizing nodal connection of the intern
 al network\, one gets to utilize the nonlinear behavior of\nphysical syste
 ms and gets to focus on optimizing a minimal number parameters. In 2021\, 
 Goto et al [1] investigated\na physical reservoir computer in the context 
 of a flow past a cylinder and shown that the computer’s computational\nc
 apability is maximized at the bifurcation point between the generation of 
 twin vortex and the onset of Karman vortex.\nIn this exposition\, the auth
 ors illustrated how the the dynamics of twin vortex affects the ability of
  the computer to\naccomplish certain tasks. In particular\, they have show
 n that the length of the twin vortex is directly proportional to\nthe perf
 ormance.\nIn this talk\, a shape optimization problem that aims to increas
 e the said capability will be presented. The op-\ntimization problem is a 
 naive formulation by maximizing two types of functional which has been his
 torically used a\nquantifiers of vortex\, namely\, the L2-norm of the curl
  of the velocity and the positivity of the determinant of the velocity\ngr
 adient. The optimization problem is regularized by a perimeter functional 
 which acts as a Tikhonov regularizer. A\nvolume constraint is also imposed
 \, which — together with the regularizer — prevents possible topologic
 al changes in\nthe domain. The analysis of this problem includes existence
  analysis of the governing state\, establishing the existence\nof shape so
 lutions\, and sensitivity of the objective functional with respect to doma
 in perturbation. We shall then utilize\nthe results of the sensitivity ana
 lysis to a gradient descent-type algorithm for numerical illustrations.\n\
 n[1] K. Goto\, K. Nakajima\, and H. Notsu\, Twin vortex computer in fluid 
 flow\, New J. Phys.\, 23 (2021)\, p. 063051\,\nhttps://doi.org/doi.org/10.
 1088/1367-2630/ac024d.\n
LOCATION:https://researchseminars.org/talk/NSCM/78/
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