Dear all,
We are happy to invite you all to the next NOMADS (Numerical ODEs, Matrix Analysis and Data Science) seminar at GSSI. This week we will have two talks, as per the following schedule:
1) Christian Lubich, University of Tuebingen, Germany Wednesday November 18, 17h00 (CET)
2) Patricia Diaz De Alba, Gran Sasso Science Institute, Italy Friday November 20, 17h15 (CET)
All seminars take place via Zoom. See below for additional information (e.g. title, abstract and zoom link). 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 and Friday!
Francesco Tudisco and Nicola Guglielmi
--------------------------------------------------------------------- November 18, 2020 (Wednesday) at 17h00 (Italian time) Christian Lubich https://na.uni-tuebingen.de/~lubich/ *Dynamical low-rank approximation* This talk reviews differential equations and their numerical solution on manifolds of low-rank matrices or of tensors with a rank structure such as tensor trains or general tree tensor networks. These low-rank differential equations serve to approximate, in a data-compressed format, large time-dependent matrices and tensors or multivariate functions that are either given explicitly via their increments or are unknown solutions to high-dimensional evolutionary differential equations, with multi-particle time-dependent Schrödinger equations and kinetic equations such as Vlasov equations as noteworthy examples of applications. Recently developed numerical time integrators are based on splitting the projection onto the tangent space of the low-rank manifold at the current approximation. In contrast to all standard integrators, these projector-splitting methods are robust to the unavoidable presence of small singular values in the low-rank approximation. This robustness relies on exploiting geometric properties of the manifold of low-rank matrices or tensors: in each substep of the projector-splitting algorithm, the approximation moves along a flat subspace of the low-rank manifold. In this way, high curvature due to small singular values does no harm. This talk is based on work done intermittently over the last decade with Othmar Koch, Bart Vandereycken, Ivan Oseledets, Emil Kieri, Hanna Walach and Gianluca Ceruti. Zoom link https://us02web.zoom.us/j/83782294125 Add event to Google calendar https://calendar.google.com/event?action=TEMPLATE&tmeid=MW83YTByZm1ia2E0MGp0YnFjMDMyNm8ydGogZ3NzaS5pdF92bG1ibnRyMDU4OXZjdDdtb2lmdHRnMTlwa0Bn&tmsrc=gssi.it_vlmbntr0589vct7moifttg19pk%40group.calendar.google.com ------------------------------------------------------------------- ------------------------------------------------------------------- November 20, 2020 (Friday) at 17h30 (Italian time) Patricia Diaz De Alba http://bugs.unica.it/~patricia/ *Numerical treatment for inverse electromagnetic problems* Electromagnetic induction surveys are among the most popular techniques for non-destructive investigation of soil properties, in order to detect the presence of both ground inhomogeneities and particular substances. Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Based on a non-linear forward model used to describe the interaction between an electromagnetic field and the soil, the aim is to reconstruct the distribution of either the electrical conductivity or the magnetic permeability with respect to depth. To this end, the inversion of both the real (in-phase) and the imaginary (quadrature) components of the signal are studied by a regularized damped Gauss-Newton method. The regularization part of the algorithm is based on a low-rank approximation of the Jacobian of the non-linear model. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. An algorithm for a regularization method that promotes the sparsity of the reconstructed electrical conductivity or magnetic permeability distribution is available. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The whole inversion algorithm has been enclosed in a MATLAB package, called FDEMtools, allowing the user to experiment with synthetic and experimental data sets, and different regularization strategies, in order to compare them and draw conclusions. The numerical effectiveness of the inversion procedure is demonstrated on synthetic and real datasets by using FDEMtools package. Zoom link https://us02web.zoom.us/j/85165138386 Add event to Google calendar https://calendar.google.com/event?action=TEMPLATE&tmeid=N2gxdW1xOGhjOTZsa2J2dWQ4YW5lb3I3bGIgZ3NzaS5pdF92bG1ibnRyMDU4OXZjdDdtb2lmdHRnMTlwa0Bn&tmsrc=gssi.it_vlmbntr0589vct7moifttg19pk%40group.calendar.google.com --------------------------------------------------------------------
— Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io