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.

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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

We consider strong temperature effects on two-phase immiscible flow through a porous medium. A dependency on temperature is introduced via a temperature-dependent viscosity for one of the phases. The purpose is to develop a simple prototype model for simulating the injection of steam into a porous medium, which is saturated with highly viscous oil. To solve the problem, a Galerkin finite element model is formulated, with special residual-based terms added to stabilise the problem when advective transport processes dominate and to capture the discontinuities that develop at oil-water interfaces. It is also discussed how the mathematical representation of the numerical model can be transformed into computer code automatically, and two test cases are presented that demonstrate that this simplified model can capture typically observed phenomena robustly.

/pdf/modelling-temperature-effects-on-multiphase-flow-through-41t3b4zc75.pdf

Modelling temperature effects on multiphase flow through porous media

Problems in solid mechanics constitute perhaps the largest field of application of finite element methods. The vast majority of solid mechanics problems involve the standard momentum balance equation, posed in a Lagrangian setting, with different models distinguished by the choice of nonlinear or linearized kinematics, and the constitutive model for determining the stress. For some common models, the constitutive relationships are rather complex. This chapter addresses a number of canonical solid mechanics models in the context of automated modeling, and focuses on some pertinent issues that arise due to the nature of the constitutive models. The solution of equations with second-order time derivatives, which characterizes dynamic problems, is also considered.

Applications in solid mechanics

A numerical model is presented for the geometrically nonlinear analysis of laminated composite materials. The formulation is derived in a consistent fashion from nonlinear continuum mechanics. The finite element formulation is briefly described, and a range of examples elucidate the performance and potential of the model. It is shown that geometric instabilities due to delamination can be captured with unstructured finite element meshes.

Garth N. Wells

Papers

Modelling temperature effects on multiphase flow through porous media

Applications in solid mechanics

A Large Strain Discontinuous Finite Element Approach to Laminated Composites

Supporting material for the paper 'CO2 dissolution in a background hydrological flow'

DOLFIN: A general-purpose finite element library