Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.

/pdf/taking-the-human-out-of-the-loop-a-review-of-bayesian-4olcznoudw.pdf

Taking the Human Out of the Loop: A Review of Bayesian Optimization

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

https://hal.archives-ouvertes.fr/hal-01461938/document

Extended finite element method for cohesive crack growth

A discontinuous Galerkin method has been developed for strain gradientdependent damage. The strength of this method lies in the fact that it allows the use of C 0 interpolation functions for continuum theories involving higherorder derivatives, while in a conventional framework at least C 1 interpolations are required. The discontinuous Galerkin formulation thereby offers significant potential for engineering computations with strain gradient-dependent models. When using basis functions with a low degree of continuity, jump conditions arise at element edges which are incorporated in the weak form. In addition to the formulation itself, a detailed study of the convergence properties of the method for various element types is presented, an error analysis is undertaken, and the method is also shown to work in two dimensions.

A discontinuous Galerkin method for strain gradient-dependent damage: Study of interpolations, convergence and two dimensional problems

The processes that are involved in migration and extraction of melt from the mantle are not yet fully understood. Gaining a better understanding of material properties of partially molten rock could help shed light on the behavior of melt on larger scales in the mantle. In this study, we simulate three-dimensional torsional deformation of a partially molten rock that contains a rigid, spherical inclusion. We compare the computed porosity patterns to those found in recent laboratory experiments. The laboratory experiments show emergence of melt-rich bands throughout the rock sample, and pressure shadows around the inclusion. The numerical model displays similar melt-rich bands only for a small bulk-to-shear-viscosity ratio (five or less). The results are consistent with earlier two-dimensional numerical simulations; however, we show that it is easier to form melt-rich bands in three dimensions compared to two. The addition of strain-rate dependence of the viscosity causes a distinct change in the shape of pressure shadows around the inclusion. This change in shape presents an opportunity for experimentalists to identify the strain-rate dependence and therefore the dominant deformation mechanism in torsion experiments with inclusions.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015GC006061

Torsion of a cylinder of partially molten rock with a spherical inclusion: theory and simulation

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the ve- locity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appro- priate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations.

Energy stable and momentum conserving hybrid finite element method for the incompressible

The FEniCS Project is a widely used, open-source problem solving environment for partial differential equations that allows users to specify equations in mathematical symbolic form via a domain-specific language, and solve them using the finite element method. The FEniCS Problem solving environment provides C++ and Python interfaces, and relies on automated code generation to reconcile expressive input with high performance. Because of the generic nature of the software, many different scientific problems are being addressed using FEniCS/DOLFIN, including geodynamics, heat flow, elasticity, electromagnetics, flow in porous media, Navier–Stokes equations and acoustics. The key aims of this project were to enhance the applicability and usability of DOLFIN, the core finite element library in the FEniCS Project, on parallel architectures. DOLFIN already supported fully distributed computation via MPI, but lacked some important infrastructure for enabling large scale parallel computation. This included a lack of (i) scalable parallel I/O and (ii) parallel mesh refinement. In addition, (iii) DOLFIN did not support threaded operations in combination with MPI. Implementation of the three aforementioned points formed the objectives of this project. All three objectives have been realised and exceeded, and the computer code developed is publicly available. Outcomes of this project are either already in a release of DOLFIN or are in development repositories and will be included in the next release, and are already being used in a number of research projects, including projects supported by UK research councils. ∗Email: chris@bpi.cam.ac.uk †Email: gnw20@cam.ac.uk

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Expressive and scalable finite element simulation beyond 1000 cores

Embedded discontinuity formulations have been recently presented as a method of incorporating displacement discontinuities in standard finite elements. These elements allow inelastic deformations to be modelled using discrete constitutive models at an internal interface. However, the actual formulation of these models is identical in concept to more traditional fracture energy regularised smeared crack models. Rather than adjusting the hardening modulus depending on element size, the inelastic strain itself is made dependent on element size. It is shown here that the embedded discontinuity idea and smeared crack models are conceptually identical.

https://repository.tudelft.nl/islandora/object/uuid%3A542fdde9-5b61-4b47-b104-4e41174acf31/datastream/OBJ/download

Garth N. Wells

Papers

A discontinuous Galerkin method for strain gradient-dependent damage: Study of interpolations, convergence and two dimensional problems

Torsion of a cylinder of partially molten rock with a spherical inclusion: theory and simulation

Energy stable and momentum conserving hybrid finite element method for the incompressible

Expressive and scalable finite element simulation beyond 1000 cores

On the conceptual equivalence of embedded strong discontinuity and smeared crack formulations