A review of nonlinear FFT-based computational homogenization methods

Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform

Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations

In this thesis we develop algorithms for the numerical solution of problems from nonlinear optimum experimental design (OED) for parameter estimation in differential–algebraic equations. These OED problems can be formulated as special types of path- and control- constrained optimal control (OC) problems. The objective is to minimize a functional on the covariance matrix of the model parameters that is given by first-order sensitivities of the model equations. Additionally, the objective is nonlinearly coupled in time, which make OED problems a challenging class of OC problems. For their numerical solution, we propose a direct multiple shooting parameterization to obtain a structured nonlinear programming problem (NLP). An augmented system of nominal and variational states for the model sensitivities is parameterized on multiple shooting intervals and the objective is decoupled by means of additional variables and constraints. In the resulting NLP, we identify several structures that allow to evaluate derivatives at greatly reduced costs compared to a standard OC formulation. For the solution of the block-structured NLPs, we develop a new sequential quadratic programming (SQP) method. Therein, partitioned quasi-Newton updates are used to approximate the block-diagonal Hessian of the Lagrangian. We analyze a model problem with indefinite, block-diagonal Hessian and prove that positive definite approximations of the individual blocks prevent superlinear convergence. For an OED model problem, we show that more and more negative eigenvalues appear in the Hessian as the multiple shooting grid is refined and confirm the detrimental impact of positive definite Hessian approximations. Hence, we propose indefinite SR1 updates to guarantee fast local convergence. We develop a filter line search globalization strategy that accepts indefinite Hessians based on a new criterion derived from the proof of global convergence. BFGS updates with a scaling strategy to prevent large eigenvalues are used as fallback if the SR1 update does not promote convergence. For the solution of the arising sparse and nonconvex quadratic subproblems, a parametric active set method with inertia control within a Schur complement approach is developed. It employs a symmetric, indefinite LBL T -factorization for the large, sparse KKT matrix and maintains and updates QR-factors of a small and dense Schur complement. The new methods are complemented by two C++ implementations: muse transforms an OED or OC problem instance to a structured NLP by means of direct multiple shooting. A special feature is that fully independent grids for controls, states, path constraints, and measurements are maintained. This provides higher flexibility to adapt the NLP formulation to the characteristics of the problem at hand and facilitates comparison of different formulations in the light of the lifted Newton method. The software package blockSQP is an implementation of the new SQP method that uses a newly developed variant of the quadratic programming solver qpOASES. Numerical results are presented for a benchmark collection of OED and OC problems that show how SR1 approximations improve local convergence over BFGS. The new method is then applied to two challenging OED applications from chemical engineering. Its performance compares favorably to an available existing implementation

Apprentissage à grande échelle et applications

This thesis presents my main research activities in statistical machine learning aftermy PhD, starting from my post-doc at UC Berkeley to my present research position atInria Grenoble. The first chapter introduces the context and a summary of my scientificcontributions and emphasizes the importance of pluri-disciplinary research. For instance,mathematical optimization has become central in machine learning and the interplay betweensignal processing, statistics, bioinformatics, and computer vision is stronger thanever. With many scientific and industrial fields producing massive amounts of data, theimpact of machine learning is potentially huge and diverse. However, dealing with massivedata raises also many challenges. In this context, the manuscript presents differentcontributions, which are organized in three main topics.Chapter 2 is devoted to large-scale optimization in machine learning with a focus onalgorithmic methods. We start with majorization-minimization algorithms for structuredproblems, including block-coordinate, incremental, and stochastic variants. These algorithmsare analyzed in terms of convergence rates for convex problems and in terms ofconvergence to stationary points for non-convex ones. We also introduce fast schemesfor minimizing large sums of convex functions and principles to accelerate gradient-basedapproaches, based on Nesterov’s acceleration and on Quasi-Newton approaches.Chapter 3 presents the paradigm of deep kernel machine, which is an alliance betweenkernel methods and multilayer neural networks. In the context of visual recognition, weintroduce a new invariant image model called convolutional kernel networks, which is anew type of convolutional neural network with a reproducing kernel interpretation. Thenetwork comes with simple and effective principles to do unsupervised learning, and iscompatible with supervised learning via backpropagation rules.Chapter 4 is devoted to sparse estimation—that is, the automatic selection of modelvariables for explaining observed data; in particular, this chapter presents the result ofpluri-disciplinary collaborations in bioinformatics and neuroscience where the sparsityprinciple is a key to build intepretable predictive models.Finally, the last chapter concludes the manuscript and suggests future perspectives.Ce mémoire présente mes activités de recherche en apprentissage statistique après mathèse de doctorat, dans une période allant de mon post-doctorat à UC Berkeley jusqu’àmon activité actuelle de chercheur chez Inria. Le premier chapitre fournit un contextescientifique dans lequel s’inscrivent mes travaux et un résumé de mes contributions, enmettant l’accent sur l’importance de la recherche pluri-disciplinaire. L’optimisation mathématiqueest ainsi devenue un outil central en apprentissage statistique et les interactionsavec les communautés de vision artificielle, traitement du signal et bio-informatiquen’ont jamais été aussi fortes. De nombreux domaines scientifiques et industriels produisentdes données massives, mais les traiter efficacement nécessite de lever de nombreux verrousscientifiques. Dans ce contexte, ce mémoire présente différentes contributions, qui sontorganisées en trois thématiques.Le chapitre 2 est dédié à l’optimisation à large échelle en apprentissage statistique.Dans un premier lieu, nous étudions plusieurs variantes d’algorithmes de majoration/minimisationpour des problèmes structurés, telles que des variantes par bloc de variables,incrémentales, et stochastiques. Chaque algorithme est analysé en terme de taux deconvergence lorsque le problème est convexe, et nous montrons la convergence de ceux-civers des points stationnaires dans le cas contraire. Des méthodes de minimisation rapidespour traiter le cas de sommes finies de fonctions sont aussi introduites, ainsi que desalgorithmes d’accélération pour les techniques d’optimisation de premier ordre.Le chapitre 3 présente le paradigme des méthodes à noyaux profonds, que l’on peutinterpréter comme un mariage entre les méthodes à noyaux classiques et les techniquesd’apprentissage profond. Dans le contexte de la reconnaissance visuelle, ce chapitre introduitun nouveau modèle d’image invariant appelé réseau convolutionnel à noyaux, qui estun nouveau type de réseau de neurones convolutionnel avec une interprétation en termesde noyaux reproduisants. Le réseau peut être appris simplement sans supervision grâceà des techniques classiques d’approximation de noyaux, mais est aussi compatible avecl’apprentissage supervisé grâce à des règles de backpropagation.Le chapitre 4 est dédié à l’estimation parcimonieuse, c’est à dire, à la séléction automatiquede variables permettant d’expliquer des données observées. En particulier, cechapitre décrit des collaborations pluri-disciplinaires en bioinformatique et neuroscience,où le principe de parcimonie est crucial pour obtenir des modèles prédictifs interprétables.Enfin, le dernier chapitre conclut ce mémoire et présente des perspectives futures

Simulation of electric field-assisted nanowire growth from aqueous solutions

The present work is aimed at investigating the mechanisms of nanowire growth from aqueous solutions through a physical and chemical modeling. Based on this modeling, deriving an optimized process control is intended. The work considers two methods of nanowire growth. The first is the dielectrophoretic nanowire assembly from neutral molecules or metal clusters. Secondly, in the directed electrochemical nanowire assembly metal-containing ions are reduced in an AC electric field in the vicinity of the nanowire tip and afterwards deposited at the nanowire surface. To describe the transport and growth processes, continuum models are employed. Furthermore, it has been necessary to consider electro-kinetic fluid flows to match the experimental observations. The occurring partial differential equations are solved numerically by means of finite element method (FEM). The effect of the process parameters on the nanowire growth are analyzed by comparing experimental results to a parameter study. The evaluation has yielded that an AC electro-osmotic fluid flow has a major influence on the dielectrophoretic nanowire assembly regarding the growth velocity and morphology. In the case of directed electrochemical nanowire assembly, the nanowire morphology can be controlled by the applied AC signal shape. Based on the nanowire growth model, an optimized AC signal has been designed, whose parametrization allows to adjust to the chemical precursor and the desired nanowire diameter.Ziel der vorliegenden Arbeit ist es, mittels physikalischer und chemischer Modelle die Mechanismen des Nanodrahtwachstums aus wässrigen Lösungen zu erforschen und daraus eine optimierte Prozesskontrolle abzuleiten. Dabei werden zwei Verfahren des Nanodrahtwachstums näher betrachtet: Dies sind die dielektrophoretische Assemblierung von neutralen Molekülen oder Metallclustern sowie die gerichtete elektrochemische Nanodrahtabscheidung (engl. directed electrochemical nanowire assembly), bei der metallhaltige Ionen im elektrischen Wechselfeld an der Nanodrahtspitze zunächst reduziert und anschließend als Metallatome abgeschieden werden. Zur Beschreibung der Transport- und Wachstumsprozesse werden Kontinuumsmodelle eingesetzt. Darüber hinaus hat es sich als notwendig erwiesen, elektrokinetische Fluidströmungen zu berücksichtigen, um die experimentellen Beobachtungen zu reproduzieren. Die auftretenden partiellen Differenzialgleichungen werden mittels der Finiten Elemente Methode (FEM) numerisch gelöst. Die Auswirkungen der Prozessparameter auf das Nanodrahtwachstum werden durch den Vergleich von experimentellen Ergebnissen mit Parameterstudien analysiert. Die Auswertung hat ergeben, dass für das dielektrophoretische Wachstum ein durch Wechselfeldelektroosmose (engl. AC electro-osmosis) angetriebener Fluidstrom die Drahtwachstumsgeschwindigkeit und -morphologie maßgeblich beeinflusst. Im Falle der gerichteten elektrochemischen Nanodrahtabscheidung lässt sich die Drahtmorphologie über das angelegte elektrische Wechselsignal steuern. Unter Verwendung des Wachstumsmodells ist ein optimiertes Signal generiert worden, dessen Parametrisierung eine gezielte Anpassung auf den chemischen Ausgangsstoff und den gewünschten Drahtdurchmesser erlaubt

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world

Sensors, measurement fusion and missile trajectory optimisation

When considering advances in “smart” weapons it is clear that air-launched systems have adopted an integrated approach to meet rigorous requirements, whereas air-defence systems have not. The demands on sensors, state observation, missile guidance, and simulation for air-defence is the subject of this research. Historical reviews for each topic, justification of favoured techniques and algorithms are provided, using a nomenclature developed to unify these disciplines. Sensors selected for their enduring impact on future systems are described and simulation models provided. Complex internal systems are reduced to simpler models capable of replicating dominant features, particularly those that adversely effect state observers. Of the state observer architectures considered, a distributed system comprising ground based target and own-missile tracking, data up-link, and on-board missile measurement and track fusion is the natural choice for air-defence. An IMM is used to process radar measurements, combining the estimates from filters with different target dynamics. The remote missile state observer combines up-linked target tracks and missile plots with IMU and seeker data to provide optimal guidance information. The performance of traditional PN and CLOS missile guidance is the basis against which on-line trajectory optimisation is judged. Enhanced guidance laws are presented that demand more from the state observers, stressing the importance of time-to-go and transport delays in strap-down systems employing staring array technology. Algorithms for solving the guidance twopoint boundary value problems created from the missile state observer output using gradient projection in function space are presented. A simulation integrating these aspects was developed whose infrastructure, capable of supporting any dynamical model, is described in the air-defence context. MBDA have extended this work creating the Aircraft and Missile Integration Simulation (AMIS) for integrating different launchers and missiles. The maturity of the AMIS makes it a tool for developing pre-launch algorithms for modern air-launched missiles from modern military aircraft.EThOS - Electronic Theses Online ServiceGBUnited Kingdo