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

This article considers the iterative solution of a finite element discretization of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyze, and numerically test an Elman, Silvester, and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optimality of the preconditioner. The presented analysis highlights the dependence of the preconditioner on parameters in the magma dynamics equations that can affect convergence of iterative linear solvers. The analysis is verified through a range of two- and three- dimensional numerical examples on unstructured grids, from simple illustrative problems through to large problems on subduction zone-like geometries. The computer code to reproduce all numerical examples is freely available as supporting material.

/pdf/analysis-of-block-preconditioners-for-models-of-coupled-1ozxkmyirk.pdf

Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics

At the grain boundaries of plastically deforming polycrystals, strain transfer mechanisms can accommodate the shear strain carried by slip bands and mechanical twins to prevent stress build-ups and damage. So far, only the accommodation obtained through slip (and twinning) alone has been considered in the mechanism known as slip (and twin) transfer. Here, a strain transfer mechanism that also requires the rotation of the crystal lattice is demonstrated. A region of accumulated slip develops perpendicular to the active slip plane in the impinged grain. The slip gradients enable a localized lattice rotation that accommodates the shear strain in the incoming band, preventing the build-up of interfacial stresses. The mechanism operates preferentially at the boundaries between highly misoriented grains. Facilitating strain transfer at these interfaces opens up new possibilities to improve the mechanical properties of polycrystals, as discussed.

/pdf/a-new-mechanism-of-strain-transfer-in-polycrystals-ckwmqzfdwf.pdf

A new mechanism of strain transfer in polycrystals.

During CO2 sequestration into a deep saline aquifer of finite vertical extent, CO2 will tend to accumulate in structural highs such as offered by an anticline. Over times of tens to thousands of years, some of the CO2 will dissolve into the underlying groundwater to produce a region of relatively dense, saturated water directly below the plume of CO2 . Continued dissolution then requires the supply of unsaturated aquifer water. In an aquifer of finite vertical extent, this may be provided by a background hydrological flow, or a laterally-spreading buoyancy-driven flow caused by the greater density of the CO2

saturated water relative to the original aquifer water.

We investigate long time steady-state dissolution in the presence of a background hydrological flow. In steady state, the distribution of CO2
in the groundwater upstream of the aquifer involves a balance between three competing effects: (i) the buoyancy-driven flow of CO2 saturated water; (ii) the diffusion of CO2 from saturated to under-saturated water; and (iii) the advection associated with the oncoming background flow. This leads to three limiting regimes. In the limit of very slow diffusion, a nearly static intrusion of dense fluid may extend a finite distance upstream, balanced by the pressure gradient associated with the oncoming background flow. In the limit of fast diffusion relative to the flow, a gradient zone may become established in which the along-aquifer diffusive flux balances the advection associated with the background flow. However, if the buoyancy-driven flow speed exceeds the background hydrological flow speed, then a third, intermediate regime may become established. In this regime, a convective recirculation develops upstream of the anticline involving the vertical diffusion of CO2 from an upstream propagating flow of dense CO2 saturated water into the downstream propagating flow of CO2 unsaturated water. For each limiting case, we find analytical solutions for the distribution of CO2 upstream of the anticline, and test our analysis with full numerical simulations. A key result is that, although there may be very different controls on the distribution and extent of CO2 bearing water upstream of the anticline, in each case the dissolution rate is given by the product of the background volume flux and the difference in concentration between the CO2 saturated water and the original aquifer water upstream.

dissolution in a background hydrological flow

This article considers the iterative solution of a finite element discretisation of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyse and numerically test a Elman, Silvester and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optimality of the preconditioner. The presented analysis highlights the dependence of the preconditioner on parameters in the magma dynamics equations that can affect convergence of iterative linear solvers. The analysis is verified through a range of two- and three-dimensional numerical examples on unstructured grids, from simple illustrative problems through to large problems on subduction zone-like geometries. The computer code to reproduce all numerical examples is freely available as supporting material.

Garth N. Wells

Papers

Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics

A new mechanism of strain transfer in polycrystals.

dissolution in a background hydrological flow

Analysis of block-preconditioners for models of coupled magma/mantle dynamics

fiat: The Finite Element Automated Tabulator