1 citations · 1 across the 4 of their papers we have counts for
5 papers
Low-rank cross approximation of function-valued tensors for reduced-order modeling of parametric PDEs
Stanislav Budzinskiy, Vladimir Kazeev, Maxim Olshanskii
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field,…
Symplectic QTT-FEM solution of the one-dimensional acoustic wave equation in the time domain
Sara Fraschini, Vladimir Kazeev, Ilaria Perugia
Structured Finite Element Methods (FEMs) based on low-rank approximation in the form of the so-called Quantized Tensor Train (QTT) decomposition (QTT-FEM) have been proposed and ex…
Limitations of neural network training due to numerical instability of backpropagation
Clemens Karner, Vladimir Kazeev, Philipp Christian Petersen
We study the training of deep neural networks by gradient descent where floating-point arithmetic is used to compute the gradients. In this framework and under realistic assumption…
Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions
V. Kazeev, I. Oseledets, M. Rakhuba +1
Homogenization in terms of multiscale limits transforms a multiscale problem with asymptotically separated microscales posed on a physical domain int…
Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs
Markus Bachmayr, Vladimir Kazeev
Folding grid value vectors of size into th order tensors of mode sizes , combined with low-rank representation in the tensor train format, has been…