A NAIVE FORMULATION OF MAXIMIZING THE COMPUTATIONAL CAPABILITY OF THE TWIN VORTEX COMPUTER VIA SHAPE OPTIMIZATION

John Simon (Institute of Mathematics, Czech Academy of Sciences)

14-Nov-2022, 14:40-16:10 (16 months ago)

Abstract: Physical reservoir computing is a new computational paradigm based on recurrent neural networks where instead of optimizing nodal connection of the internal network, one gets to utilize the nonlinear behavior of physical systems and gets to focus on optimizing a minimal number parameters. In 2021, Goto et al [1] investigated a physical reservoir computer in the context of a flow past a cylinder and shown that the computer’s computational capability is maximized at the bifurcation point between the generation of twin vortex and the onset of Karman vortex. In this exposition, the authors illustrated how the the dynamics of twin vortex affects the ability of the computer to accomplish certain tasks. In particular, they have shown that the length of the twin vortex is directly proportional to the performance. In this talk, a shape optimization problem that aims to increase the said capability will be presented. The op- timization problem is a naive formulation by maximizing two types of functional which has been historically used a quantifiers of vortex, namely, the L2-norm of the curl of the velocity and the positivity of the determinant of the velocity gradient. The optimization problem is regularized by a perimeter functional which acts as a Tikhonov regularizer. A volume constraint is also imposed, which — together with the regularizer — prevents possible topological changes in the domain. The analysis of this problem includes existence analysis of the governing state, establishing the existence of shape solutions, and sensitivity of the objective functional with respect to domain perturbation. We shall then utilize the results of the sensitivity analysis to a gradient descent-type algorithm for numerical illustrations.

[1] K. Goto, K. Nakajima, and H. Notsu, Twin vortex computer in fluid flow, New J. Phys., 23 (2021), p. 063051, doi.org/doi.org/10.1088/1367-2630/ac024d.

MathematicsPhysics

Audience: researchers in the topic

( video )


Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).

Organizers: Miloslav Feistauer, Petr Knobloch, Martin Kružík*, Šárka Nečasová*
*contact for this listing

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