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Gegeben sei für ein binäres Klassifikationsproblem ein künstliches, neuronales Netzwerk ann bestehend aus ReLUKnoten und linearen Schichten (convolution, pooling, fully connected). Das Netzwerk ann sei mit hinreichender Genauigkeit an Hand von Trainingsdaten trainiert. Wir werden zeigen, dass ein solches Netzwerk in verschiedene Partitionen des Eingaberaums zerlegt werden kann, wobei jede Partition eine lineare Abbildung der Eingabewerte auf einen klassifizierenden Ausgabewert repräsentiert. Im Weiteren gehen wir von einem einfachen Netzwerk ann aus, bei dem die Eingangswerte Mintermen von Attributwerten entsprechen. Einfach ist ein Netzwerk, wenn es für eine geringe Anzahl von Attributen trainiert wurde und die Anzahl der ReLU-Knoten ebenfalls gering ist. In der Arbeit wird gezeigt, dass jede lineare Partition durch einen CQQL-Ausdruck beschrieben werden kann. Ein CQQL-Ausdruck lässt sich mit Hilfe von Quantenlogik-inspirierten Entscheidungsbäumen beschreiben.
Physics-informed neural networks (PINN) are machine-learning methods that have been proved to be very successful and effective for solving governing equations of fluid flow. In this work we develop a robust and efficient model within this framework and apply it to a series of two-dimensional three-component (2D3C) stereo particle-image velocimetry datasets, to reconstruct the mean velocity field and correct measurements errors in the data. Within this framework, the PINNsbased model solves the Reynolds-averaged-Navier-Stokes (RANS) equations for zeropressure-gradient turbulent boundary layer (ZPGTBL) without a prior assumption and only taking the data at the PIV domain boundaries. The TBL data has different flow conditions upstream of the measurement location due to the effect of an applied flow control via uniform blowing. The developed PINN model is very robust, adaptable and independent of the upstream flow conditions due to different rates of wall-normal blowing while predicting the mean velocity quantities simultaneously. Hence, this approach enables improving the mean-flow quantities by reducing errors in the PIV data. For comparison, a similar analysis has been applied to numerical data obtained from a spatially-developing ZPGTBL and an adverse-pressure-gradient (APG) TBL over a NACA4412 airfoil geometry. The PINNs-predicted results have less than 1% error in the streamwise velocity and are in excellent agreement with the reference data. This shows that PINNs has potential applicability to shear-driven turbulent flows with different flow histories, which includes experiments and numerical simulations for predicting high-fidelity data.
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent differential equations, one can apply the recently developed method of domain segmentation. That is, the domain may be split into several subdomains, on which the optimisation problem is solved. In classic adaptive numerical methods, the mesh as well as the domain may be refined or decomposed, in order to improve the accuracy. Also, the degree of approximation accuracy may be adapted. Therefore, it is desirable to transfer such important and successful strategies to the field of neural-network-based solutions. In the presented work, we propose a novel adaptive neural approach to meet this aim for solving time-dependent problems. To this end, each subdomain is reduced in size until the optimisation is resolved up to a predefined training accuracy. In addition, while the neural networks employed are by default small, we propose a means to adjust also the number of neurons in an adaptive way. We introduce conditions to automatically confirm the solution reliability and optimise computational parameters whenever it is necessary. Results are provided for several initial-value problems that illustrate important computational properties of the method.
Die Bachelorarbeit beschäftigt sich mit der Entwicklung effizienter Methoden für die Klassifizierung der Stadien von Zellen. Hierbei liegt der Fokus auf sogenannten Deep-Learning-Algorithmen. Diese haben sich unter anderem in der Bilderkennung als sehr leistungsfähig erwiesen und können genutzt werden, um große Mengen von mikroskopischen Zellbildern in kurzer Zeit zu klassifizieren. Aufgezeigt werden Möglichkeiten zur Optimierung solcher Algorithmen mit dem Ziel, Genauigkeit und Speichergröße zu verbessern. Es wurden hierbei der Einfluss von verschiedenen Parametern auf die Performance eines Algorithmus untersucht und gegenübergestellt, verschiedene etablierte Modelle miteinander verglichen und eine Auswahl gängiger Methoden zur Modell-Optimierung getestet. Genutzt wurde die Software-Bibliothek TensorFlow, welche über die Programmiersprache Python angesprochen wird. Reale Anwendungsdaten wurden von der Firma Medipan zur Verfügung gestellt.
Machine learning is a field that has been the object of study of many researchers around the globe during the last decades. Very often to solve machine learning challenges like classification problems for example, one needs to train an artificial neural network. To train this network a certain loss function has to be minimized. There is a ubiquitous approach to achieve this which consists of using variants of the stochastic gradient descent combined with the backpropagation algorithm. In our work, we aimed at testing a rather non-conventional scheme consisting of making use of the solvers a software called AMPL offers.
Reconstruction of the 3D shape information is a fundamental problem in computer vision. Among different shape recovering technologies, photometric stereo is highlighted for its capability to produce high quality 3D reconstruction. This dissertation generalizes photometric stereo in different aspects towards creating a practical 3D reconstruction. The proposed techniques can be considered as a fundamental support to develop future cameras offering 3D shapes for various applications such as movie and video game industry, medical sciences, virtual reality, automotive driving and etc. The first generalization is developed for addressing specularities in 3D reconstructions and also involving the perspective projection. These attempts lead to remove the limitation of working with diffuse materials and confined projected scenes. We will prove the applicability of our approach using complex scenes like endoscopy images. In the second proposed approach, we will offer a real-time 3D reconstruction of micro-details with a more generalized reflectance model. Moreover, a recurrent optimization network will be provided. These innovations lead to presenting the 3D reconstruction of details which are even invisible to human eyes like micro-prints on the banknote. This information recovery can be used in various areas such as detecting security items on financial documents for fraud detection and also the quality control of any industrial productions including delicate details such as printed circuits. In the third proposed model, we develop a PS reconstruction technique using neural networks for the uncalibrated PS where the light direction is not available. Finally, for the first time, benefiting from deep neural networks and meta heuristic algorithms, we will devise an approach which can deliver high qualified 3D shape from the internet and out-door images, without any pre-necessary knowledge.
For many countries, gasturbine technology is one of the key technologies for the reduction of climate-damaging pollutant emissions. The profitability of such facilities, however, is highly dependent on the price for the utilized fossil fuel, which is why there is a constant need for increased efficiency. The potential of increasing the efficiency of the individual components is basically limited by factors which will reduce operating life. The goal of this thesis is to develop methods for improved automated structural design optimization, which shall be developed on the basis of compressor airfoils. Special attention is payed to avoid the excitation of failure critical eigenmodes by detecting them automatically. This is achieved by introducing a method based on self-organizing neural networks which enables the projection of eigenmodes of arbitrary airfoil geometries onto standard surfaces, thereby making them comparable. Another neural network is applied to identify eigenmodes which have been defined as critical for operating life. The failure rate of such classifiers is significantly reduced by introducing a newly developed initialization method based on principle components. A structural optimization is set up which shifts the eigenfrequency bands of critical modes in such a way that the risk of resonance with engine orders is minimized. In order to ensure practical relevance of optimization results, the structural optimization is coupled with an aerodynamic optimization in a combined process. Conformity between the loaded hot-geometry utilized by the aerodynamic design assessment and the unloaded cold-geometry utilized by the structural design assessment is ensured by using loaded-to-unloaded geometry transformation. Therefor an innovative method is introduced which, other than the established time-consuming iterative approach, uses negative density for a direct transformation taking only a few seconds, hence, making it applicable to optimization. Additionally, in order for the optimal designs to be robust against manufacturing variations, a method is developed which allows to assess the maximum production tolerance of a design from which onwards possible design variations are likely to violate design constraints. In contrast to the usually applied failure rate, the production tolerance is a valid requirement for suppliers w.r.t.~expensive parts produced in low-quantity, and therefore is a more suitable optimization objective.
In der vorliegenden Arbeit wird die Eignung von Künstlichen Neuronalen Netzen hinsichtlich der Modellierung des komplexen Prozessverhaltens in einer Flachglasschmelzanlage analysiert. Die Identifikation und das Training der neuronalen Prozessmodelle erfolgen mit Messdaten einer Schmelzwanne für Flachglas. Im Vordergrund steht die Evaluation einer geeigneten Netzstruktur und die Parametrierung der Netzparameter. Dabei wird der Einfluss der einzelnen Netzparameter in Bezug auf die Genauigkeit der Netze eingehend untersucht. Anhand von Testdaten wird nachgewiesen, dass die qualitätsbestimmenden Temperaturen und der Glasstand mit Künstlichen Neuronalen Netzen hinreichend genau berechnet werden können.
Auf Basis der entwickelten neuronalen Prozessmodelle wird anschließend eine modellbasierte prädiktive Regelstrategie beschrieben. Neben der Auswahl des Gütekriteriums und des Optimierungsalgorithmus zur Berechnung zukünftiger Stellgrößen werden Richtlinien zur Dimensionierung der verfügbaren Reglerparameter abgeleitet.
The first part of this thesis is devoted to the evaluation of approaches which exploit the inherent redundancy of the speech signal to improve the noise robustness. On the basis of this evaluation on the AURORA 2000 database, we further study in detail two of the evaluated approaches. The first of these approaches is the hybrid RBF/HMM approach, which is an attempt to combine the superior classification performance of radial basis functions (RBFs) with the ability of HMMs to model time variation. The second approach is using neural networks to non-linearly reduce the dimensionality of large feature vectors including context frames. We propose the use of different MLP topologies for that purpose. Experiments on the AURORA 2000 database reveal that the performance of the first approach is similar to the performance of systems based on SCHMMs. The second approach cannot outperform the performance of linear discriminant analysis (LDA) on a database recorded in real car environments, but it is on average significantly better than LDA on the AURORA 2000 database.
Ein wesentlicher Aspekt der Dynamik elektrischer Aktivitaet in neuronalen Gewebe betrifft die Ausbreitung von Aktivitaet in Form von Wellen. In dieser Arbeit untersuchen wir die Existenz und Eigenschaften laufender Wellenloesungen einer nichtlinearen Neuronalen-Feld-Gleichung. Das Modell beruecksichtigt die nichtlokalen synaptischen Verbindungen und die Zeitverzoegerung bei der Kommunikation zwischen den Nervenzellen, die abstandsabhaengig ist. Die Modellgleichung hat daher die mathematische Form einer nichtlinearer, retardierter Integralgleichung. In der Arbeit wird zuerst gezeigt, wie man die Modellgleichung durch ein System von partiellen Differentialgleichungen approximieren kann, das leichter numerisch untersucht werden kann. Anschliessend werden laufende Wellenloesungen des Modells numerisch und analytisch untersucht.