La simulation numérique des écoulements (CFD) est largement utilisée aujourd'hui dans l'industrie aéronautique, de l'avant-projet à la conception des appareils. En parallèle, la puissance des calculateurs s'est accrue, permettant d'effectuer des simulations résolvant les équations de Navier-Stokes moyennées (RANS) dans un délai de restitution acceptable du point de vue industriel. Cependant, les configurations simulées sont de plus en plus complexes géométriquement, rendant la réalisation du maillage très coûteuse en temps humain. Notre objectif est de proposer une méthode permettant de simplifier la génération de maillages autour de géométries complexes, en exploitant les avantages de la méthode Chimère, tout en levant les difficultés principales rencontrées par cette méthode dans le calcul des connectivités. Dans notre approche, le domaine de calcul est découpé en régions proches et en régions éloignées des corps. Des grilles curvilignes de faible extension décrivent les régions autour des corps. Le maillage de fond est défini par un ensemble de grilles cartésiennes superposées aux grilles de corps, qui sont engendrées et adaptées automatiquement selon les caractéristiques de l'écoulement. Afin de traiter des maillages recouvrants autour de géométries complexes sans surcoût humain, les différentes grilles sont regroupées par composant Chimère. Des relations d'assemblage sont alors définies entre composants, en s'inspirant de la Géométrie de Construction des Solides (CSG), où un solide peut être construit par opérations booléennes successives entre solides primitifs. Le calcul des connectivités Chimère est alors réalisé de manière simplifiée. Des simulations RANS sont effectuées autour d'un fuselage d'hélicoptère avec mât de soufflerie et autour d'une aile NACA0015 en incidence, afin de mettre en oeuvre la méthode. / Computational fluid dynamics (CFD) is widely used today in aeronautics, while the computing power has increased, enabling to perform simulations solving Reynolds-averaged Navier-Stokes equations (RANS) within an acceptable time frame from the industrial point of view. However, the configurations are more and more geometrically complex, making the mesh generation step prohibitive. Our aim is here to propose a method enabling a simplification of the mesh generation over complex geometries, taking advantage of the Chimera method and overcoming the major difficulties arising when performing overset grid connectivity. In our approach, the computational domain is partitioned into near-body regions and off-body regions. Near-body regions are meshed by curvilinear grids of short extension describing the obstacles involved in the simulation. Off-body mesh is defined by a set of adaptive Cartesian grids, overlapping near-body grids. In order to consider overset grids over complex geometries with no additional cost, grids are gathered by Chimera component, and assembly relations are defined between them, inspired by Constructive Solid Geometry, where a solid can result from boolean operations between primitive solids. The overset grid connectivity is thus simplified. RANS simulations are performed over a helicopter fuselage with a strut, and over a NACA0015 wing.

MRI (Magnetic Resonance Imaging) is a medical imaging method that uses magnetic fields in order to retrieve images of the human body. This thesis revolves around a novel acquisition method of 3D fMRI (functional Magnetic Resonance Imaging) called PRESTO-CAN that uses a radial pattern in order to sample the (kx,kz)-plane of k-space (the frequency domain), and a Cartesian sample pattern in the ky-direction. The radial sample pattern allows for a denser sampling of the central parts of k-space, which contain the most basic frequency information about the structure of the recorded object. This allows for higher temporal resolution to be achieved compared with other sampling methods since a fewer amount of total samples are needed in order to retrieve enough information about how the object has changed over time. Since fMRI is mainly used for monitoring blood flow in the brain, increased temporal resolution means that we can be able to track fast changes in brain activity more efficiently.The temporal resolution can be further improved by reducing the time needed for scanning, which in turn can be achieved by applying parallel imaging. One such parallel imaging method is SENSE (SENSitivity Encoding). The scan time is reduced by decreasing the sampling density, which causes aliasing in the recorded images. The aliasing is removed by the SENSE method by utilizing the extra information provided by the fact that multiple receiver coils with differing sensitivities are used during the acquisition. By measuring the sensitivities of the respective receiver coils and solving an equation system with the aliased images, it is possible to calculate how they would have looked like without aliasing.In this master thesis, SENSE has been successfully implemented in PRESTO-CAN. By using normalized convolution in order to refine the sensitivity maps of the receiver coils, images with satisfying quality was able to be reconstructed when reducing the k-space sample rate by a factor of 2, and images of relatively good quality also when the sample rate was reduced by a factor of 4. In this way, this thesis has been able to contribute to the improvement of the temporal resolution of the PRESTO-CAN method. / MRI (Magnetic Resonance Imaging) är en medicinsk avbildningsmetod som använder magnetfält för att framställa bilder av människokroppen. Detta examensarbete kretsar kring en ny inläsningsmetod för 3D-fMRI (functional Magnetic Resonance Imaging) vid namn PRESTO-CAN som använder ett radiellt mönster för att sampla (kx,kz)-planet av k-rummet (frekvensdomänen), och ett kartesiskt samplingsmönster i ky-riktningen. Det radiella samplingsmönstret möjliggör tätare sampling av k-rummets centrala delar, som innehåller den mest grundläggande frekvensinformationen om det inlästa objektets struktur. Detta leder till att en högre temporal upplösning kan uppnås jämfört med andra metoder eftersom det krävs ett mindre antal totala sampel för att få tillräcklig information om hur objektet har ändrats över tid. Eftersom fMRI framförallt används för att övervaka blodflödet i hjärnan innebär ökad temporal upplösning att vi kan följa snabba ändringar i hjärnaktivitet mer effektivt.Den temporala upplösningen kan förbättras ytterligare genom att minska scanningstiden, vilket i sin tur kan uppnås genom att tillämpa parallell avbildning. En metod för parallell avbildning är SENSE (SENSitivity Encoding). Scanningstiden minskas genom att minska samplingstätheten, vilket orsakar vikning i de inlästa bilderna. Vikningen tas bort med SENSE-metoden genom att utnyttja den extra information som tillhandahålls av det faktum att ett flertal olika mottagarspolar med sinsemellan olika känsligheter används vid inläsningen. Genom att mäta upp känsligheterna för de respektive mottagarspolarna och lösa ett ekvationssystem med de vikta bilderna är det möjligt att beräkna hur de skulle ha sett ut utan vikning.I detta examensarbete har SENSE framgångsrikt implementerats i PRESTO-CAN. Genom att använda normaliserad faltning för att förfina mottagarspolarnas känslighetskartor har bilder med tillfredsställande kvalitet varit möjliga att rekonstruera när samplingstätheten av k-rummet minskats med en faktor 2, och bilder med relativt bra kvalitet också när samplingstätheten minskats med en faktor 4. På detta sätt har detta examensarbete kunnat bidra till förbättrandet av PRESTO-CAN-metodens temporala upplösning.

Dans cette thèse, nous nous sommes intéressés à des écoulements complexes où les régimes hydrodynamique et raréfiés coexistent. On retrouve ce type d'écoulements dans des applications industrielles comme les pompes à vide ou encore les rentrées de capsules spatiales dans l'atmosphère, lorsque la distance entre les molécules de gaz devient si grande que le comportement microscopique des molécules doit être pris en compte. Pour ce faire, nous étudions 2 modèles de l'équation de Boltzmann, le modèle BGK et le modèle ES-BGK. Dans un premier temps, nous développons une nouvelle condition au bord permettant une transition continue de la solution du régime raréfié vers le régime hydrodynamique. Cette nouvelle condition permettant de préserver l'asymptotique vers les équations d'Euler compressible est ensuite incluse dans une méthode de frontière immergée pour traiter, à une précision raisonnable (ordre 2), le cas de solides immergés dans un écoulement, sur grilles cartésiennes. L'utilisation de grillescartésiennes permet une parallélisation aisée du code de simulation numérique afin d'obtenir une réduction considérable du temps de calcul, un des principaux inconvénients des modèles cinétiques. Par la suite, une approche dites aux grilles locales en vitesses est présentée réduisant également le temps de calcul de manière importante (jusqu'à 80%). Des simulations 3D sont également présentées montrant l'efficacité des méthodes. Enfin, le transport passive de particules solides dans un écoulement raréfié est étudié avec l'introduction d'un modèle de type Vlasov couplé au modèle cinétique. Grâce à une résolution basée sur des méthodes de remaillage, la pollution de dispositif optiques embarqués sur des satellites dues à des particules issues de la combustion incomplète dans les moteurs contrôlant d'altitude est étudiée. / This work is devoted to the study of complex flows where hydrodynamic and rarefled regimes coexist. This kind of flows are found in vacuum pumps or hypersonic re-entries of space vehicles where the distance between gas molecules is so large that their microscopicbehaviour differ from the average behaviour of the flow and has be taken into account. We then consider two modelsof the Boltzmann equation viable for such flows: the BGK model dans the ES-BGK model.We first devise a new wall boundary condition ensuring a smooth transition of the solution from the rarefled regime to the hydrodynamic regime. We then describe how this boundary condition (and boundary conditions in general) can be enforced with second order accuracy on an immersed body on Cartesian grids preserving the asymptotic limit towards compressible Euler equations. We exploit the ability of Cartesian grids to massive parallel computations (HPC) to drastically reduce the computational time which is an issue for kinetic models. A new approach considering local velocity grids is then presented showing important gain on the computational time (up to 80%). 3D simulations are also presented showing the efficiency of the methods. Finally, solid particle transport in a rarefied flow is studied. The kinetic model is coupled with a Vlasov-type equation modeling the passive particle transport solved with a method based on remeshing processes. As application, we investigate the realistic test case of the pollution of optical devices carried by satellites due to incompletely burned particles coming from the altitude control thrusters

On s’intéresse à la simulation d’écoulements compressibles multi-matériaux et, notamment, aux interactions fluide/structure dans les régimes transitoires et en dynamique rapide. Le but est de pouvoir décrire l’évolution de matériaux de lois de comportement très différentes à l’aide d’un modèle unique. Les milieux sont seulement différenciés par leurs équations d’état et sont séparés par une interface dite sharp. Les matériaux peuvent être des fluides ou des solides élastiques et sont soumis à de grandes déformations. Le modèle est écrit dans le formalisme eulérien. Le schéma numérique est résolu sur des grilles cartésiennes pour des simulations en trois dimensions.Une extension du modèle permet de décrire les déformations plastiques des solides. / We are interested in the simulation of compressible multimaterial flows and especially influid/structure interactions in transient states and fast dynamics. We aim to describe the evolution of materials of very different constitutive laws with an unified model. The materials are only differentiated by their own constitutive laws and are separated by a sharp interface. They can be as well fluids or elastic solids and under go large de formations. The model is written in the Eulerian framework. The numerical scheme is solved on Cartesian grids for simulations in three dimensions. An extension of the elastic model is added to describe the plastic deformations of solids.

This thesis is concerned with the utilization of formal verification techniques in the design of the functional approximations of combinational circuits. We thoroughly study the existing formal approaches for the approximate equivalence checking and their utilization in the approximate circuit development. We present a new method that integrates the formal techniques into the Cartesian Genetic Programming. The key idea of our approach is to employ a new search strategy that drives the evolution towards promptly verifiable candidate solutions. The proposed method was implemented within ABC synthesis tool. Various parameters of the search strategy were examined and the algorithm's performance was evaluated on the functional approximations of multipliers and adders with operand widths up to 32 and 128 bits respectively. Achieved results show an unprecedented scalability of our approach.

This Master's Thesis is focused on the principles of neural networks, primarily convolutional neural networks (CNN). It introduces the evolutionary optimization in the context of neural networks. One of existing libraries devoted to the CNN design was chosen (Keras), analysed and used in image classification tasks. An optimization technique based on cartesian genetic programming that should reduce the complexity of CNN's computation was proposed and implemented. The impact of the proposed technique on CNN behaviour was evaluated in a case study.

This thesis examines a conversion of a solution produced by geometric semantic genetic programming (GSGP) to an instantion of cartesian genetic programming (CGP). GSGP has proven its quality to create complex mathematical models; however, the size of these models can get problematically large. CGP, on the other hand, is able to reduce the size of given models. This thesis combinated these methods to create a subtree CGP (SCGP). The SCGP uses an output of GSGP as an input and the evolution is performed using the CGP. Experiments performed on four pharmacokinetic tasks have shown that the SCGP is able to reduce the solution size in every case. Overfitting was detected in one out of four test problems.

This thesis deals with image classification based on genetic programming and coevolution. Genetic programming algorithms make generating executable structures possible, which allows us to design solutions in form of programs. Using coevolution with the fitness prediction lowers the amount of time consumed by fitness evaluation and, therefore, also the execution time. The thesis describes a theoretical background of evolutionary algorithms and, in particular, cartesian genetic programming. We also describe coevolutionary algorithms properties and especially the proposed method for the image classifier evolution using coevolution of fitness predictors, where the objective is to find a good compromise between the classification accuracy, design time and classifier complexity. A part of the thesis is implementation of the proposed method, conducting the experiments and comparison of obtained results with other methods.

This thesis is focused on finding procedures that would accelerate symbolic regressions in Cartesian Genetic Programming. It describes Cartesian Genetic Programming and its use in the task of symbolic regression. It deals with the SIMD architecture and the SSE and AVX instruction set. Several optimizations that lead to a significant acceleration of evolution in Cartesian Genetic Programming are presented. A method of a bit-level parallel simulation that uses AVX2 vectors allows to process 256 input combinations of a logic circuit in paralell. Similarly it is possible to use a byte-level parallel simulation and work with 32 bytes when evolving an image filter. A new method of batch mutation can accelerate the evolution of combinational logic circuits thousand times depending on the problem size. For example, using a combination of these and other methods the evolution of 5 x 5b multipliers took 5.8 seconds on average on an Intel Core i5-4590 processor.

The aim of this work is to design and implement a method for the evolutionary design of neural networks with generative encoding. The proposed method is based on J. F. Miller's approach and uses a brain model that is gradually developed and which allows extraction of traditional neural networks. The development of the brain is controlled by programs created using cartesian genetic programming. The project was implemented in Python with the use of Numpy library. Experiments have shown that the proposed method is able to construct neural networks that achieve over 90 % accuracy on smaller datasets. The method is also able to develop neural networks capable of solving multiple problems at once while slightly reducing accuracy.