SSD - Hoefler Seminar
Prof. Dr. Torsten Hoefler - High-Performance Communication in Machine Learning
One of the main drivers behind the rapid recent advances in machine learning has been the availability of efficient system support.
Despite existing progress, scaling compute-intensive machine learning workloads to a large number of compute nodes is still a challenging task. In this talk, we provide an overview of communication aspects in deep learning. We address the communication challenge, by proposing SparCML, a general, scalable communication layer for machine learning applications. SparCML is built on the observation that many distributed machine learning algorithms either have naturally sparse communication patterns, or have updates which can be sparsified in a structured way for improved performance, without loss of convergence or accuracy. To exploit this insight, we analyze, design, and implement a set of communication-efficient protocols for sparse input data, in conjunction with efficient machine learning algorithms which can leverage these primitives. Our communication protocols generalize standard collective operations, by allowing processes to contribute sparse input data vectors, of heterogeneous sizes. Our generic communication layer is enriched with additional features, such as support for non-blocking
(asynchronous) operations and support for low-precision data representations. We validate our algorithmic results experimentally on a range of large-scale machine learning applications and target architectures, showing that we can leverage sparsity for order-of-magnitude runtime savings, compared to existing methods and frameworks.
SSD - Banda Seminar- CANCELED
Prof. Dr. Mapundi Banda - A Lyapunov Approach to Boundary Feedback Stabilisation for Hyperbolic Balance Laws: a Numerical Perspective
Department for Mathematics and Applied Mathematics, University of Pretoria, South Africa
First-order systems of evolution models governed by time-dependent hyperbolic partial dierential equations will be considered. In this talk we will present a review of the Lyapunov approach for boundary feedback stabilisation for such dierential equations. The rst part of the presentation will give an overview of recent results in the mathematical analysis of stabilisation of hyperbolic balance laws. The second part will then discuss a numerical approach to discretise the balance laws. This will be followed by a numerical analysis for the discrete Lyapunov approach. A selection of examples will be discussed and the eectiveness of the numerical stabilisation will also be demonstrated.
EU Regional School - Holzapfel Seminar
Prof. Dr. Gerhard Holzapfel - Models for Fiber-Reinforced Elastic Solids with a Focus on Soft Biological Tissues
Institute of Biomechanics, Graz University of Technology, Austria
This short course provides a summary of models for fiber-reinforced elastic solids with distributed fiber orientations. As a motivation we start with a simple 1D problem which we then develop further to 3D considering a 3D isotropic fiber dispersion, perfectly aligned fibers, a rotationally symmetric dispersion and a non-rotationally symmetric dispersion. We review basic elements from the nonlinear theory of continuum mechanics that is required in the modeling of fiber-reinforced elastic solids. Of particular relevance are the structure tensors and related deformation invariants required to consider fibers and their dispersed directions in constitutive models. We also provide computational aspects needed for finite element implementation of the discussed models, and focus on an efficient formulation which avoids non-physical responses in the numerical analysis of anisotropic materials. The effect of the fiber structure on the material response is discussed on the basis of several examples. We discuss changes of the fiber structure in images obtained from cardiovascular tissues in health and disease using high-resolution optical microscopy. Related finite-element simulations highlight the need to incorporate the structural differences of soft biological (fibrous) tissues.
SSD - Hughes Seminar-CANCELED
Prof. Thomas J.R. Hughes, Ph.D. - The Isogeometric Approach to Analysis
Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, USA
The vision of Isogeometric Analysis was first presented in a paper published October 1, 2005 . Since then it has become a focus of research within both the fields of Finite Element Analysis (FEA) and Computer Aided Design (CAD) and is rapidly becoming a mainstream analysis methodology and a new paradigm for geometric design . The key concept utilized in the technical approach is the development of a new foundation for FEA, based on rich geometric descriptions originating in CAD, resulting in a single geometric model that serves as a basis for both design and analysis.
In this overview, I will describe some areas in which progress has been made in developing improved methodologies to efficiently solve problems that have been at the very least difficult, if not impossible, within traditional FEA. I will also describe current areas of intense activity and areas where problems remain open, representing both challenges and opportunities for future research (see, e.g., [3,4]).
 T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135-4195.
 J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, U.K., 2009.
 Special Issue on Isogeometric Analysis, (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 284, (1 February 2015), 1-1182.
 Special Issue on Isogeometric Analysis: Progress and Challenges, (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 316, (1 April 2017), 1-1270.
EU Regional School - Huerta Seminar
Prof. Antonio Huerta, Ph.D. - Low and High-order Approximations of Parameterized Engineering Problems in Computational Solid and Fluid Mechanics
Department of Applied Mathematics III, Universitat Politècnica de Catalunya, Spain
In the first part, an overview of recent advances on modern hybrid discretization approaches, namely the face-centered finite volume (FCFV) and the hybridizable discontinuous Galerkin (HDG) methods, are presented. The former is an efficient low-order approach that has been shown to be extremely robust to mesh distortion and stretching, which are usually responsible for the degradation of classical finite volume solutions [R. Sevilla, M. Giacomini, and A. Huerta. “A face-centred finite volume method for second-order elliptic problems” Int. J. Numer. Methods Eng. 115(8), pp. 986-1014 (2018). R. Sevilla, M. Giacomini, and A. Huerta. “A locking-free face-centred finite volume (FCFV) method for linear elasticity” arXiv:1806.07500 (2018)]. The latter is a high-order strategy originally proposed in [B. Cockburn, J. Gopalakrishnan, and R. Lazarov. “Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems" SIAM J. Numer. Anal. 47(2):1319–1365 (2009)]. Recently, an alternative high-order HDG formulation allowing the pointwise fulfillment of the conservation of angular momentum has been proposed. This aspect is crucial in the approximation of problems in computational solid and fluid mechanics in which quantities of engineering interest (e.g. compliance and aeronautical forces) have to be evaluated starting from the stress tensor. [R. Sevilla, M. Giacomini, A. Karkoulias, and A. Huerta. “A superconvergent hybridisable discontinuous Galerkin method for linear elasticity” Int. J. Numer. Methods Eng. 116(2), pp. 91-116 (2018). M. Giacomini, A. Karkoulias, R. Sevilla, and A. Huerta. “A superconvergent HDG method for Stokes flow with strongly enforced symmetry of the stress tensor” arXiv:1802.09394 (2018)].
In the second part, the proper generalized decomposition (PGD) is employed to devise efficient separated representations of the solution of parameterized engineering problems. The resulting PGD-based computational vademecums allow the fast evaluation of solutions involving user-supplied data, such as boundary conditions and geometrical configurations of the domain.