Dear all,
We hope you all had joyful holidays and wish you all a great start for the new year!
We are ready to start with this year's NOMADS seminar at GSSI and would like to invite you to this week's talk. The seminar will be given on Wednesday January 13 at 17:00 (CET) by Gianluca Ceruti from University of Tuebingen. Title, abstract and zoom link are below. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/
Please feel free to distribute this announcement as you see fit.
Hope to see you all on Wednesday! Francesco and Nicola
================================ Speaker: Gianluca Ceruti, University of Tuebingen https://na.uni-tuebingen.de/~ceruti/
Zoom link: https://us02web.zoom.us/j/82131676880
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