Good morning everyone,

This is just a gentle reminder about today's seminar "Numerical integrators for dynamical low-rank approximation" by Gianluca Ceruti (Uni Tuebingen). Abstract below.

The seminar is at 17:00 (CET). To attend please use the zoom link: https://us02web.zoom.us/j/82131676880

Hope to see you there! Francesco and Nicola

----------- Gianluca Ceruti https://na.uni-tuebingen.de/~ceruti/ - University of Tuebingen

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