This is just a gentle reminder about today's seminar "Numerical
integrators for dynamical low-rank approximation" by Gianluca Ceruti
(Uni Tuebingen). Abstract below.
Numerical integrators for dynamical low-rank approximation
Discretization of time-dependent high-dimensional PDEs suffers of an
undesired effect, known as curse of dimensionality. The amount of
data to be stored and treated, grows exponentially, and exceeds
standard capacity of common computational devices.
In this setting, time dependent model order reductions techniques
are desirable.
In the present seminar, together with efficient numerical
integrators, we present a recently developed approach: dynamical
low-rank approximation.
Dynamical low-rank approximation for matrices will be firstly
presented, and a numerical integrator with two remarkable properties
will be introduced: the matrix projector splitting integrator.
Based upon this numerical integrator, we will construct two
equivalent extensions for tensors, multi-dimensional arrays, in
Tucker format - a high-order generalization of the SVD decomposition
for matrices. These extensions are proven to preserve the excellent
qualities of the matrix integrator.
To conclude, via a novel compact formulation of the Tucker
integrator, we will further extend the matrix and Tucker projector
splitting integrators to the most general class of Tree Tensor
Networks. Important examples belonging to this class and of interest
for applications are given, but not only restricted to, by Tensor
Trains.
This seminar is based upon a joint work with Ch. Lubich and H.
Walach.
—
Francesco Tudisco
Assistant Professor
School of Mathematics
GSSI Gran Sasso Science Institute
Web: https://ftudisco.gitlab.io