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Equivariance and structure preservation in numerical methods; some cases and viewpoints

Presented by: 
Brynjulf Owren
Date: 
Wednesday 11th December 2019 - 15:05 to 15:50
Venue: 
INI Seminar Room 2
Abstract: 
Our point of departure is the situation when
there is a group of transformations acting both on our problem space and on the
space in which our computations are produced. Equivariance happens when the map
from the problem space to the computation space, i.e. our numerical method,
commutes with the group action. This is a rather general and vague definition,
but we shall make it precise and consider a few concrete examples in the talk.
In some cases, the equivariance property is natural, in other cases it is
something that we want to impose in the numerical method in order to obtain
computational schemes with certain desired structure preserving qualities. Many
of the examples we present will be related to the numerical solution of
differential equations and we may also present some recent examples from
artificial neural networks and discrete integrable systems. This is work in
progress and it summarises some of the ideas the speaker has been discussing
with other participants this autumn.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons