Andrea Di Blasio – Coupled Mathematical Models for Heart Integration : a Stability Study
EPFL supervisors: Prof. A. Quarteroni, T. Lassila
In this thesis, we consider a fully coupled model which aims at reproducing some qualitative features of the electro-mechanical activity of the heart. The models used to describe both the electrical and mechanical activities are relatively simple. However, coupling them together can give rise to numerical instabilities or incorrect predictions. After having introduced each of the sub-models of the fully coupled system we perform some numerical experiments to draw some insights on the numerical approximation of this problem. Firstly we focus on the numerical approximation of the Aliev-Panfilov model, which controls the electrical activation of the muscle. We verify that different approaches can be followed to solve such a problem by the finite element method reducing the computational effort. However each approach can lead to inaccurate predictions of the front velocity. Then we suggest also two numerical schemes for time integration particularly suited for PDEs such as the Aliev-Panfilov model: the operator splitting method and the Runge-Kutta-Chebyshev method. When considering the fully coupled problem, we examine two ways of reducing the computational cost: treating some of the coupling terms explicitly or solving the linearised system iteratively. We verify that with the first choice we can experience numerical instabilities depending on the numerical scheme used for time integration. On the other hand, when solving the linearised system iteratively, key points to solve the problem efficiently are the choice of an adaptive stopping criterion and a good preconditioner. From the numerical experiments performed we conclude that the coupling between the active stress and the mechanics is very influential on the stability of the system and on the convergence of the residuals.
Elena Queirolo : Isogeometric Analysis for Navier-Stokes equations
EPFL supervisor : Dr Luca Dede’
About WIAS, Berlin
Responsible : Prof. John Volker
In this project, we present some applications of Isogeometric Analysis in stationary fluid dynamics problems. Specifically, we focus on the numerical solution of the Stokes and Navier- Stokes equations and the fulfillment of the inf-sup conditions, in particular by computing the Brezzi and Babuška inf-sup constants. The Isogeometric Taylor-Hood spaces are presented and the stability of the Stokes and Navier-Stokes equations has been numerically tested in a variety of settings, including smooth NURBS basis functions and the multiple patches case.
Ivan Slijepcevic – Improving Learning Efficiency in Large Scale Neural Networks
EPFL supervisors : Prof. Wulfram Gerstner – Carlos Stein Naves de Brito
About Sony Deutschland GmbH (Stuttgart Technology Center)
Responsible : Dr. Thomas Kemp
In the last decade, artificial neural networks have reached their peak performance and are now considered as state of the art for numerous tasks. While being intensively used in various application areas, their computational complexity remains an issue. This project investigates several techniques for reducing the training time of neural networks on the use-case of creating a statistical language model. Language model gives us the probability of observing next word in a sequence given the observed history, and its main use
lays in speech recognition systems.
The main computational bottleneck is implied by the vocabulary of the target language, because the neural network needs to have an output for every word in a vocabulary and all the outputs need to be coupled in order to produce a probability distribution. First chosen technique approximates the computation in the network’s last layer using only the most contributing outputs, the second one randomly samples which outputs to train per iteration, and the third splits the words into several classes in order to train a special smaller network for each class in parallel. The last approach shows the best performance and is able to provide a multiple times speedup.
Laurent Fasnacht – Next-generation Video Coding for Embedded Parallel Computing
EPFL supervisor : Dr MER Marco Mattavelli
Responsible : Dr Giorgio Zoia
Compression is one of the major stakes in video processing. A new recommandation, HEVC/H.265, was released in April 2013.This master thesis shows how to parallelize an HEVC/H.265 encoder, in order to fully exploit the large number of computing cores of nowadays computers.More specifically, two mechanisms are considered, tiles and wavefronts. Both methods trade some compression efficiency for parallelism.Moreover, it will be shown that wavefronts are not very efficient when processing “small” images with a large number of CPUs. One solution to this problem is to process multiple frames in parallel, using overlapped wavefronts. An implementation of these techniques is presented, as an extension of an open source HEVC encoder, along with some important software engineering aspects which should not be neglected. Finally, the efficiency of the implementation of these different methods is measured.