Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances. When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries. Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation. In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme. The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

Šio darbo tyrimų sritis yra duomenų tyryba remiantis daugiamačių duomenų vizualia analize. Tai leidžia tyrėjui betarpiškai dalyvauti duomenų analizės procese, geriau pažinti sudėtingus duomenis ir priimti geriausius sprendimus. Disertacijos tikslas yra sukurti metodą tokios duomenų projekcijos radimui plokštumoje, kad tyrėjas galėtų pamatyti ir įvertinti daugiamačių taškų tarpgrupinius panašumus/skirtingumus. Šiam tikslui pasiekti yra pasiūlytas radialinių bazinių funkcijų ir daugiasluoksnio perceptrono, turinčio ,,butelio kaklelio“ neuroninio tinklo savybes, junginys. Naujas tinklas naudojamas vizualiai daugiamačių duomenų analizei, kai atidėjimui plokštumoje arba trimatėje erdvėje taškai gaunami paskutinio paslėpto neuronų sluoksnio išėjimuose, kai į tinklo įėjimą paduodami daugiamačiai duomenys. Šio tinklo ypatybė yra ta, kad gautas vaizdas plokštumoje labiau atspindi bendrą duomenų struktūrą (klasteriai, klasterių tarpusavio artumas, taškų tarpklasterinis panašumas) nei daugiamačių taškų tarpusavio išsidėstymą. / The area of research is data mining based on multidimensional data visual analysis. This allows researcher to participate in the process of data analysis directly, to understand the complex data better and to make the best decisions. The objective of the dissertation is to create a method for making a multidimensional data projection on the plane such that the researcher could see and assess the intergroup similarities and differences of multidimensional points. In order to achieve the target, a new hybrid neural network is proposed and investigated. This neural network integrates the ideas both of the radial basis function neural network and that of a multilayer perceptron, which has the properties of a ''bottleneck'' neural network. The new network is used for the visual analysis of multidimensional data in such a way that the output values of the neurons of the last hidden layer are the two-dimensional or three-dimensional projections of the multidimensional data, when the multidimensional data is given to the network. A peculiarity of the network is that the visualization results on the plane reflect the general structure of the data (clusters, proximity between clusters, intergroup similarities of points) rather than the location of multidimensional points.

The area of research is data mining based on multidimensional data visual analysis. This allows researcher to participate in the process of data analysis directly, to understand the complex data better and to make the best decisions. The objective of the dissertation is to create a method for making a multidimensional data projection on the plane such that the researcher could see and assess the intergroup similarities and differences of multidimensional points. In order to achieve the target, a new hybrid neural network is proposed and investigated. This neural network integrates the ideas both of the radial basis function neural network and that of a multilayer perceptron, which has the properties of a ''bottleneck'' neural network. The new network is used for the visual analysis of multidimensional data in such a way that the output values of the neurons of the last hidden layer are the two-dimensional or three-dimensional projections of the multidimensional data, when the multidimensional data is given to the network. A peculiarity of the network is that the visualization results on the plane reflect the general structure of the data (clusters, proximity between clusters, intergroup similarities of points) rather than the location of multidimensional points. / Šio darbo tyrimų sritis yra duomenų tyryba remiantis daugiamačių duomenų vizualia analize. Tai leidžia tyrėjui betarpiškai dalyvauti duomenų analizės procese, geriau pažinti sudėtingus duomenis ir priimti geriausius sprendimus. Disertacijos tikslas yra sukurti metodą tokios duomenų projekcijos radimui plokštumoje, kad tyrėjas galėtų pamatyti ir įvertinti daugiamačių taškų tarpgrupinius panašumus/skirtingumus. Šiam tikslui pasiekti yra pasiūlytas radialinių bazinių funkcijų ir daugiasluoksnio perceptrono, turinčio ,,butelio kaklelio“ neuroninio tinklo savybes, junginys. Naujas tinklas naudojamas vizualiai daugiamačių duomenų analizei, kai atidėjimui plokštumoje arba trimatėje erdvėje taškai gaunami paskutinio paslėpto neuronų sluoksnio išėjimuose, kai į tinklo įėjimą paduodami daugiamačiai duomenys. Šio tinklo ypatybė yra ta, kad gautas vaizdas plokštumoje labiau atspindi bendrą duomenų struktūrą (klasteriai, klasterių tarpusavio artumas, taškų tarpklasterinis panašumas) nei daugiamačių taškų tarpusavio išsidėstymą.

Environmental simulation models have been playing a key role in civil and environmental engineering decision making processes for decades. The utility of an environmental model depends on how well the model is structured and calibrated. Model calibration is typically in an automated form where the simulation model is linked to a search mechanism (e.g., an optimization algorithm) such that the search mechanism iteratively generates many parameter sets (e.g., thousands of parameter sets) and evaluates them through running the model in an attempt to minimize differences between observed data and corresponding model outputs. The challenge rises when the environmental model is computationally intensive to run (with run-times of minutes to hours, for example) as then any automatic calibration attempt would impose a large computational burden. Such a challenge may make the model users accept sub-optimal solutions and not achieve the best model performance. The objective of this thesis is to develop innovative strategies to circumvent the computational burden associated with automatic calibration of computationally intensive environmental models. The first main contribution of this thesis is developing a strategy called “deterministic model preemption” which opportunistically evades unnecessary model evaluations in the course of a calibration experiment and can save a significant portion of the computational budget (even as much as 90% in some cases). Model preemption monitors the intermediate simulation results while the model is running and terminates (i.e., pre-empts) the simulation early if it recognizes that further running the model would not guide the search mechanism. This strategy is applicable to a range of automatic calibration algorithms (i.e., search mechanisms) and is deterministic in that it leads to exactly the same calibration results as when preemption is not applied. One other main contribution of this thesis is developing and utilizing the concept of “surrogate data” which is basically a reasonably small but representative proportion of a full set of calibration data. This concept is inspired by the existing surrogate modelling strategies where a surrogate model (also called a metamodel) is developed and utilized as a fast-to-run substitute of an original computationally intensive model. A framework is developed to efficiently calibrate hydrologic models to the full set of calibration data while running the original model only on surrogate data for the majority of candidate parameter sets, a strategy which leads to considerable computational saving. To this end, mapping relationships are developed to approximate the model performance on the full data based on the model performance on surrogate data. This framework can be applicable to the calibration of any environmental model where appropriate surrogate data and mapping relationships can be identified. As another main contribution, this thesis critically reviews and evaluates the large body of literature on surrogate modelling strategies from various disciplines as they are the most commonly used methods to relieve the computational burden associated with computationally intensive simulation models. To reliably evaluate these strategies, a comparative assessment and benchmarking framework is developed which presents a clear computational budget dependent definition for the success/failure of surrogate modelling strategies. Two large families of surrogate modelling strategies are critically scrutinized and evaluated: “response surface surrogate” modelling which involves statistical or data–driven function approximation techniques (e.g., kriging, radial basis functions, and neural networks) and “lower-fidelity physically-based surrogate” modelling strategies which develop and utilize simplified models of the original system (e.g., a groundwater model with a coarse mesh). This thesis raises fundamental concerns about response surface surrogate modelling and demonstrates that, although they might be less efficient, lower-fidelity physically-based surrogates are generally more reliable as they to-some-extent preserve the physics involved in the original model. Five different surface water and groundwater models are used across this thesis to test the performance of the developed strategies and elaborate the discussions. However, the strategies developed are typically simulation-model-independent and can be applied to the calibration of any computationally intensive simulation model that has the required characteristics. This thesis leaves the reader with a suite of strategies for efficient calibration of computationally intensive environmental models while providing some guidance on how to select, implement, and evaluate the appropriate strategy for a given environmental model calibration problem.

The hybridization of soft computing methods of Radial Basis Function (RBF) neural networks, Multi Layer Perceptron (MLP) neural networks with back-propagation learning, fuzzy sets and rough sets are studied in the scope of this thesis. Conventional MLP, conventional RBF, fuzzy MLP, fuzzy RBF, rough fuzzy MLP, and rough fuzzy RBF networks are compared. In the fuzzy neural networks implemented in this thesis, the input data and the desired outputs are given fuzzy membership values as the fuzzy properties &ldquo / low&rdquo / , &ldquo / medium&rdquo / and &ldquo / high&rdquo / . In the rough fuzzy MLP, initial weights and near optimal number of hidden nodes are estimated using rough dependency rules. A rough fuzzy RBF structure similar to the rough fuzzy MLP is proposed. The rough fuzzy RBF was inspected whether dependencies like the ones in rough fuzzy MLP can be concluded.

The time-dependent Schrödinger equation (TDSE) models the quantum nature of molecular processes.  Numerical simulations based on the TDSE help in understanding and predicting the outcome of chemical reactions. This thesis is dedicated to the derivation and analysis of efficient and reliable simulation tools for the TDSE, with a particular focus on models for the interaction of molecules with time-dependent electromagnetic fields. Various time propagators are compared for this setting and an efficient fourth-order commutator-free Magnus-Lanczos propagator is derived. For the Lanczos method, several communication-reducing variants are studied for an implementation on clusters of multi-core processors. Global error estimation for the Magnus propagator is devised using a posteriori error estimation theory. In doing so, the self-adjointness of the linear Schrödinger equation is exploited to avoid solving an adjoint equation. Efficiency and effectiveness of the estimate are demonstrated for both bounded and unbounded states. The temporal approximation is combined with adaptive spectral elements in space. Lagrange elements based on Gauss-Lobatto nodes are employed to avoid nondiagonal mass matrices and ill-conditioning at high order. A matrix-free implementation for the evaluation of the spectral element operators is presented. The framework uses hybrid parallelism and enables significant computational speed-up as well as the solution of larger problems compared to traditional implementations relying on sparse matrices. As an alternative to grid-based methods, radial basis functions in a Galerkin setting are proposed and analyzed. It is found that considerably higher accuracy can be obtained with the same number of basis functions compared to the Fourier method. Another direction of research presented in this thesis is a new algorithm for quantum optimal control: The field is optimized in the frequency domain where the dimensionality of the optimization problem can drastically be reduced. In this way, it becomes feasible to use a quasi-Newton method to solve the problem. / eSSENCE

The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution. A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail. The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required. Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.

The thesis reports a contribution to the development of neural-like network- based element-free methods for the numerical simulation of some non-Newtonian fluid flow problems. The numerical approximation of functions and solution of the governing partial differential equations are mainly based on radial basis function networks. The resultant micro-macroscopic approaches do not require any element-based discretisation and only rely on a set of unstructured collocation points and hence are truly meshless or element-free. The development of the present methods begins with the use of the multi-layer perceptron networks (MLPNs) and radial basis function networks (RBFNs) to effectively eliminate the volume integrals in the integral formulation of fluid flow problems. An adaptive velocity gradient domain decomposition (AVGDD) scheme is incorporated into the computational algorithm. As a result, an improved feed forward neural network boundary-element-only method (FFNN- BEM) is created and verified. The present FFNN-BEM successfully simulates the flow of several Generalised Newtonian Fluids (GNFs), including the Carreau, Power-law and Cross models. To the best of the author's knowledge, the present FFNN-BEM is the first to achieve convergence for difficult flow situations when the power-law indices are very small (as small as 0.2). Although some elements are still used to discretise the governing equations, but only on the boundary of the analysis domain, the experience gained in the development of element-free approximation in the domain provides valuable skills for the progress towards an element-free approach. A least squares collocation RBFN-based mesh-free method is then developed for solving the governing PDEs. This method is coupled with the stochastic simulation technique (SST), forming the mesoscopic approach for analyzing viscoelastic flid flows. The velocity field is computed from the RBFN-based mesh-free method (macroscopic component) and the stress is determined by the SST (microscopic component). Thus the SST removes a limitation in traditional macroscopic approaches since closed form constitutive equations are not necessary in the SST. In this mesh-free method, each of the unknowns in the conservation equations is represented by a linear combination of weighted radial basis functions and hence the unknowns are converted from physical variables (e.g. velocity, stresses, etc) into network weights through the application of the general linear least squares principle and point collocation procedure. Depending on the type of RBFs used, a number of parameters will influence the performance of the method. These parameters include the centres in the case of thin plate spline RBFNs (TPS-RBFNs), and the centres and the widths in the case of multi-quadric RBFNs (MQ-RBFNs). A further improvement of the approach is achieved when the Eulerian SST is formulated via Brownian configuration fields (BCF) in place of the Lagrangian SST. The SST is made more efficient with the inclusion of the control variate variance reduction scheme, which allows for a reduction of the number of dumbbells used to model the fluid. A highly parallelised algorithm, at both macro and micro levels, incorporating a domain decomposition technique, is implemented to handle larger problems. The approach is verified and used to simulate the flow of several model dilute polymeric fluids (the Hookean, FENE and FENE-P models) in simple as well as non-trivial geometries, including shear flows (transient Couette, Poiseuille flows)), elongational flows (4:1 and 10:1 abrupt contraction flows) and lid-driven cavity flows.

Thesis (M.S.) -- Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

A aproximação fisionômica é o método que busca, a partir do crânio, simular a fotografia de um indivíduo quando em vida. Deve ser empregada como último recurso, na busca de desaparecidos, quando não houver possibilidade de aplicação de um método válido de identificação. O objetivo deste estudo foi obter a aproximação fisionômica, a partir de um crânio seco e de tomografia computadorizada multislice de indivíduos vivos, através da função de base radial hermitiana (FBRH). Constituiu-se também em avaliar o resultado da mesma quanto ao reconhecimento. Na primeira etapa do estudo, foi utilizada a imagem escaneada de um crânio seco, de origem desconhecida, com o intuito de avaliar se a quantidade de pontos obtidos seria suficiente para aplicação da FBRH e consequente reconstrução da superfície facial. Na segunda fase, foram utilizadas três tomografias de indivíduos vivos, para análise da semelhança alcançada entre a face escaneada e as aproximações faciais. Nesta etapa, foi aplicada uma associação de diferentes metodologias já publicadas, para reconstrução de uma mesma região da face, a partir de um mesmo crânio. Na última etapa, foram simuladas situações de reconhecimento com familiares e amigos dos indivíduos doadores das tomografias. Observou-se que a metodologia de FBRH pode ser empregada em aproximação fisionômica. Houve reconhecimento positivo nos três sujeitos estudados, sendo que, em dois deles, os resultados foram ainda mais significativos. Desta forma, conclui-se que a metodologia é rápida, objetiva e proporciona o reconhecimento. Esta permite a criação de múltiplas versões de aproximações fisionômicas a partir do mesmo crânio, o que amplia as possibilidades de reconhecimento. Observou-se ainda que a técnica não exige habilidade artística do profissional. / Facial approximation works by building the visual face up from the skull. This method should be performed as last resort, to carry out for missing persons, when there is no other primary identification method avaliable. The purpose of this study was to introduce a new computerized method with hermite radial basis function (HRBF) for facial approximation using dry skull and computed tomography (CT). The same was also evaluated as a result of the recognition. Firstly, a scan of a dry unidentified skull image was used in order to assess if the amount of points would be sufficient for HRBF methodology and subsequent reconstruction of the facial surface. In second, three CT scans of living individuals were used to evaluate the similarity achieved between the real face scanned and facial approximations. An association of different facial structures reconstruction techniques already published for the same region of the face was applied for the same skull. Moreover, some situations from developed facial approximations were simulated, as recognition by a relative or parent, on a face pool-test. Results from the study showed that the purposed methodology can be used for facial approximation. At the three cases a correct approximation identification as one of a few possible matches to the missing person happened. In two of them, the results were consistently better at identifying the correct approximation. In conclusion, the proposed methodology is fast, objective and reaches visual identification. It is possible to perform multiple versions of the same skull, changing the selected data into the system, which maximizes the chances of establishing recognition of the target face. It was also observed that the technique does not need artistic interpretation.