Thu, 20 Feb 2020

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Learning with nonlinear Perron eigenvectors

Francesco Tudisco
(Gran Sasso Science Institute GSSI)
Abstract

In this talk I will present a Perron-Frobenius type result for nonlinear eigenvector problems which allows us to compute the global maximum of a class of constrained nonconvex optimization problems involving multihomogeneous functions.

I will structure the talk into three main parts:

First, I will motivate the optimization of homogeneous functions from a graph partitioning point of view, showing an intriguing generalization of the famous Cheeger inequality.

Second, I will define the concept of multihomogeneous function and I will state our main Perron-Frobenious theorem. This theorem exploits the connection between optimization of multihomogeneous functions and nonlinear eigenvectors to provide an optimization scheme that has global convergence guarantees.

Third, I will discuss a few example applications in network science and machine learning that require the optimization of multihomogeneous functions and that can be solved using nonlinear Perron eigenvectors.

 

 

Thu, 31 Oct 2019

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

On coarse spaces for solving the heterogenous Helmholtz equation with domain decomposition methods

Niall Bootland
(University of Strathclyde)
Abstract

The development of effective solvers for high frequency wave propagation problems, such as those described by the Helmholtz equation, presents significant challenges. One promising class of solvers for such problems are parallel domain decomposition methods, however, an appropriate coarse space is typically required in order to obtain robust behaviour (scalable with respect to the number of domains, weakly dependant on the wave number but also on the heterogeneity of the physical parameters). In this talk we introduce a coarse space based on generalised eigenproblems in the overlap (GenEO) for the Helmholtz equation. Numerical results within FreeFEM demonstrate convergence that is effectively independent of the wave number and contrast in the heterogeneous coefficient as well as good performance for minimal overlap.

Thu, 06 Jun 2019

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Parallel numerical algorithms for resilient large scale simulations

Dr Mawussi Zounon
(Numerical Algorithms Group & University of Manchester)
Abstract

As parallel computers approach Exascale (10^18 floating point operations per second), processor failure and data corruption are of increasing concern. Numerical linear algebra solvers are at the heart of many scientific and engineering applications, and with the increasing failure rates, they may fail to compute a solution or produce an incorrect solution. It is therefore crucial to develop novel parallel linear algebra solvers capable of providing correct solutions on unreliable computing systems. The common way to mitigate failures in high performance computing systems consists of periodically saving data onto a reliable storage device such as a remote disk. But considering the increasing failure rate and the ever-growing volume of data involved in numerical simulations, the state-of-the-art fault-tolerant strategies are becoming time consuming, therefore unsuitable for large-scale simulations. In this talk, we will present a  novel class of fault-tolerant algorithms that do not require any additional resources. The key idea is to leverage the knowledge of numerical properties of solvers involved in a simulation to regenerate lost data due to system failures. We will also share the lessons learned and report on the numerical properties and the performance of the new resilience algorithms.

Thu, 21 Feb 2019

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Tomographic imaging with flat-field uncertainty

Prof Martin Skovgaard Andersen
(Danish Technical University)
Abstract

Classical methods for X-ray computed tomography (CT) are based on the assumption that the X-ray source intensity is known. In practice, however, the intensity is measured and hence uncertain. Under normal circumstances, when the exposure time is sufficiently high, this kind of uncertainty typically has a negligible effect on the reconstruction quality. However, in time- or dose-limited applications such as dynamic CT, this uncertainty may cause severe and systematic artifacts known as ring artifacts.
By modeling the measurement process and by taking uncertainties into account, it is possible to derive a convex reconstruction model that leads to improved reconstructions when the signal-to-noise ratio is low. We discuss some computational challenges associated with the model and illustrate its merits with some numerical examples based on simulated and real data.

Thu, 15 Nov 2018

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Block Low-Rank Matrices: Main Results and Recent Advances

Mr Théo Mary
(Manchester University)
Abstract

In many applications requiring the solution of a linear system Ax=b, the matrix A has been shown to have a low-rank property: its off-diagonal blocks have low numerical rank, i.e., they can be well approximated by matrices of small rank. Several matrix formats have been proposed to exploit this property depending on how the block partitioning of the matrix is computed.
In this talk, I will discuss the block low-rank (BLR) format, which partitions the matrix with a simple, flat 2D blocking. I will present the main characteristics of BLR matrices, in particular in terms of asymptotic complexity and parallel performance. I will then discuss some recent advances and ongoing research on BLR matrices: their multilevel extension, their use as preconditioners for iterative solvers, the error analysis of their factorization, and finally the use of fast matrix arithmetic to accelerate BLR matrix operations.

Thu, 07 Dec 2017
14:00
Rutherford Appleton Laboratory, nr Didcot

Truncated SVD Approximation via Kronecker Summations

Professor James Nagy
(Emory University)
Abstract


In this talk we describe an approach to approximate the truncated singular value decomposition of a large matrix by first decomposing the matrix into a sum of Kronecker products. Our approach can be used to more efficiently approximate a large number of singular values and vectors than other well known schemes, such as iterative algorithms based on the Golub-Kahan bidiagonalization or randomized matrix algorithms. We provide theoretical results and numerical experiments to demonstrate accuracy of our approximation, and show how the approximation can be used to solve large scale ill-posed inverse problems, either as an approximate filtering method, or as a preconditioner to accelerate iterative algorithms.
 

Thu, 02 Nov 2017

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Point-spread function reconstruction in ground-based astronomy

Professor Raymond Chan
(Chinese University of Hong Kong)
Abstract

Because of atmospheric turbulence, images of objects in outer space acquired via ground-based telescopes are usually blurry.  One way to estimate the blurring kernel or point spread function (PSF) is to make use of the aberration of wavefront received at the telescope, i.e., the phase. However only the low-resolution wavefront gradients can be collected by wavefront sensors. In this talk, I will discuss how to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase and the PSF in high accuracy. I will end by relating the problem to high-resolution image reconstruction and methods for solving it.
Joint work with Rui Zhao and research supported by HKRGC.

Thu, 15 Jun 2017

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Discrete adjoints on many cores - algorithmic differentiation and verification for accelerated PDE solvers

Dr Jan Hückelheim
((Imperial College, London))
Abstract


Adjoint derivatives reveal the sensitivity of a computer program's output to changes in its inputs. These derivatives are useful as a building block for optimisation, uncertainty quantification, noise estimation, inverse design, etc., in many industrial and scientific applications that use PDE solvers or other codes.
Algorithmic differentiation (AD) is an established method to transform a given computation into its corresponding adjoint computation. One of the key challenges in this process is the efficiency of the resulting adjoint computation. This becomes especially pressing with the increasing use of shared-memory parallelism on multi- and many-core architectures, for which AD support is currently insufficient.
In this talk, I will present an overview of challenges and solutions for the differentiation of shared-memory-parallel code, using two examples: an unstructured-mesh CFD solver, and a structured-mesh stencil kernel, both parallelised with OpenMP. I will show how AD can be used to generate adjoint solvers that scale as well as their underlying original solvers on CPUs and a KNC XeonPhi. The talk will conclude with some recent efforts in using AD and formal verification tools to check the correctness of manually optimised adjoint solvers.
 

Thu, 18 May 2017

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Structural topology optimisation using the level set method and its applications to acoustic-structure interaction problems

Dr Renato Picelli
(Cardiff University)
Abstract

Structural optimization can be interpreted as the attempt to find the best mechanical structure to support specific load cases respecting some possible constraints. Within this context, topology optimization aims to obtain the connectivity, shape and location of voids inside a prescribed structural design domain. The methods for the design of stiff lightweight structures are well established and can already be used in a specific range of industries where such structures are important, e.g., in aerospace and automobile industries.

In this seminar, we will go through the basic engineering concepts used to quantify and analyze the computational models of mechanical structures. After presenting the motivation, the methods and mathematical tools used in structural topology optimization will be discussed. In our method, an implicit level set function is used to describe the structural boundaries. The optimization problem is approximated by linearization of the objective and constraint equations via Taylor’s expansion. Shape sensitivities are used to evaluate the change in the structural performance due to a shape movement and to feed the mathematical optimiser in an iterative procedure. Recent developments comprising multiscale and Multiphysics problems will be presented and a specific application proposal including acoustic-structure interaction will be discussed.

Thu, 23 Feb 2017

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

On Imaging Models Based On Fractional Order Derivatives Regularizer And Their Fast Algorithms

Prof. Ke Chen
(University of Liverpool)
Abstract


In variational imaging and other inverse problem modeling, regularisation plays a major role. In recent years, high order regularizers such as the total generalised variation, the mean curvature and the Gaussian curvature are increasingly studied and applied, and many improved results over the widely-used total variation model are reported.
Here we first introduce the fractional order derivatives and the total fractional-order variation which provides an alternative  regularizer and is not yet formally analysed. We demonstrate that existence and uniqueness properties of the new model can be analysed in a fractional BV space, and, equally, the new model performs as well as the high order regularizers (which do not yet have much theory). 
In the usual framework, the algorithms of a fractional order model are not fast due to dense matrices involved. Moreover, written in a Bregman framework, the resulting Sylvester equation with Toeplitz coefficients can be solved efficiently by a preconditioned solver. Further ideas based on adaptive integration can also improve the computational efficiency in a dramatic way.
 Numerical experiments will be given to illustrate the advantages of the new regulariser for both restoration and registration problems.
 

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