Military simulation is essential for modern warfare, providing a virtual environment for training, analysis, and rehearsal of procedures. Accurate correlation between simulated entities, called tracks, and their radar detections, called tracks, is crucial for generating reliable data, vital for evaluating military operations and improving training exercises. However, factors like radar noise, communication errors, and simulation inaccuracies complicate this correlation. This thesis aims to develop a robust method for correlating simulated truth entities with corresponding radar tracks in military simulations. The proposed method tackles challenges such as radar noise and communication errors to improve the reliability and validity of simulation statistics. The research encompasses the theoretical development of three correlation algorithms, one of which serves as a benchmark for verification. The methods were evaluated across various simulated scenarios, in which the two correlation methods consistently outperformed the benchmark, particularly in scenarios with fewer data points.

In this thesis, a deep learning-based surrogate model for predicting sea ice dynamics is developed that is capable of predicting linear kinematic features in a high-resolution setting. Predicting sea ice dynamics at high resolutions is critical for understanding climate patterns and enabling safe navigation in Arctic regions. Traditional continuum models based on the viscous-plastic rheology are computationally intensive when employed at high resolutions to capture linear kinematic features (LKFs), which are narrow zones of deformation in sea ice.

A supervised learning approach was adopted, focusing on convolutional neural network architectures, specifically the U-Net and a classic bottleneck model. Various loss functions were explored, including traditional metrics like the MSE and novel domain-specific functions such as the strain rate error (SRE), which incorporates physical knowledge of sea ice behaviour. The models were trained on a dataset generated from numerical simulations of sea ice dynamics on a 2 km grid.

The key findings indicate that the U-Net architecture combined with the MSE+SRE loss function outperforms other models. This architecture's depth and use of skip connections allow it to capture complex, multi-scale patterns inherent in sea ice dynamics. The integration of the SRE into the loss function significantly enhances the model's ability to predict LKFs, demonstrating the benefit of incorporating domain knowledge into machine learning models.

While the surrogate model effectively predicts LKFs for short-term forecasts up to approximately 5.5 hours (10 time steps), errors accumulate over longer periods, leading to significant errors after about 11 hours (20 time steps). However, the efficiency gain of this surrogate model is striking: the computation of 10 time steps can be done within a second, compared to the 30 minutes that traditional numerical methods need. The study also underscores the critical importance of training data selection and preparation in influencing model performance and generalisation capabilities.

In conclusion, this work demonstrates that a deep learning-based surrogate model, particularly utilising the U-Net architecture and the MSE+SRE loss function, can effectively predict sea ice dynamics at high resolutions with significant computational efficiency. The model generates forecasts within seconds, offering a viable alternative to traditional numerical simulations that require hours of computation. Future work should focus on mitigating error accumulation to extend the forecasting horizon and exploring advanced learning methods to further integrate physical insights into the modelling process.

In this thesis, gate set tomography (GST) has been conducted on the nitrogen vacancy center (NV). Gate set tomography is a protocol for characterization of logic operations (gates) on quantum computing processors. The NV’s electron served as a qubit. The quantum circuits were run both experimentally as well as on an NV-simulator. GST is different from its predecessors in the sense that it estimates all aspects of the processor simultaneously, without assuming any of its parts to be ideal. However, it does assume that the gates are Markovian. This allows to analyse the gate errors more precisely via their error generators. In addition to this, the diamond norm and a measure of the amount of model violation were used to examine the results. The electron qubit can couple to the nearby nitrogen nucleus, which can cause non-Markovian dynamics. The nitrogen nucleus (𝑆 = 1) can be initialised using nuclear spin polarization. The effects of different initialisation procedures on GST’s results were
researched. Furthermore, a dynamical decoupling XY-4 echo sequence could be employed to protect the quantum state of the qubit. How the presence of the echo affected the estimated gates and their errors was probed. It was discovered that the echo was extremely good at decreasing the amount of model violation, most likely by preventing the electron from coupling to the nitrogen, which can lead to non-Markovian dynamics. Without the echo, GST’s estimates were satisfactory only if the nitrogen nucleus was initialised with a high enough fidelity, at least 0.95. Another topic for further research would be to perform GST on the electron and the nitrogen system, by modelling the nitrogen nucleus as
a qutrit.

As the technology of quantum computers improves, the need to evaluate their performance also becomes an important tool for indexing and comparing of quantum performance. Current benchmarking proposals either focus on gate-level evaluation, are centered around a single performance metric, or only evaluate in-house quantum computers. This gives rise to the need for a holistic, application- oriented, and hardware-agnostic benchmarking tool that can provide fair and varied insight into quantum computer performance. This thesis continues the development of the QPack benchmark, which collects quantum computer data by running noisy intermediate-scale quantum (NISQ)-era applications and transforms this data into an overall performance score, which is decomposed into four subscores.

These scores are quantitative metrics of quantum performance that allow for easy and quick comparisons between different quantum computers. The QPack benchmark is an application-oriented cross-platform benchmarking suite for quantum computers and simulators, which makes use of scalable Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver applications. Using a varied set of benchmark applications, an insight into how well a quantum computer or its simulator performs on a general NISQ-era application can be quantitatively made. QPack is built on top of the cross-platform library |Lib⟩ (pronounced: libket), which allows for a single expression of a quantum circuit and execution on multiple quantum computers.

Using the QPack benchmarking scores, a comparison is made between various quantum computer simulators, running both locally and on vendors’ remote cloud services. Tested local simulators include Qiskit Aer, Cirq, Rigetti QVM, and QuEST. For remote simulators, the IBMQ, IonQ, and Rigetti simulators have been benchmarked. The QPack benchmark is also executed on the Rigetti Aspen-M-1 and a selection of available quantum hardware from the IBMQ aviary, namely the Nairobi, Jakarta, Perth, Lagos, Quito, and Manila processors. For all quantum computers, an analysis is made of their individual performance in the QPack benchmark, as well as an evaluation of how these simulators or hardware implementations compare to each other. Based on the results of the QPack benchmark, the local QuEST simulator, the remote IBMQ QASM simulator and the IBMQ Nairobi and Quito quantum computers achieve best performance compared to the other tested backends.

This work shows that the QPack benchmark is capable of providing holistic quantum computer performance for quantum computers, be it physical implementation or their simulator counterparts. The latest version of the QPack benchmark and all the results collected can be found in the repository: https://gitlab.com/libket/qpack/-/tree/stable.

The breadth of theoretical results on efficient Markov Chain Monte Carlo (MCMC) sampling schemes on discrete spaces is slim when compared to the available theory for MCMC sampling schemes on continuous spaces. Nonetheless, in [Zan17] a simple framework to design Metropolis-Hastings (MH) proposal kernels that incorporate local information about the target is presented. The class of functions for which the resulting MH kernels are Peskun optimal in high-dimensional regimes is characterized. We will refer to these functions as \textit{balancing functions} and to the class of resulting MH proposal kernels as \textit{pointwise informed proposals}. In [PG19], the class of balancing functions is used to construct Markov Jump Processes (MJP) on discrete state spaces. As a result, the Zanella process is constructed. In the absence of a theoretical result on the optimal balancing function to choose from the class of balancing functions, a heuristic approach is proposed using the Zanella process. To further encourage the mixing behaviour of the simulated chain, the algebraic structure of the state space is exploited to achieve non-reversible Markov chains on short to medium timescales. Simulations are performed for all the considered MCMC sampling schemes by studying the Bayesian record linkage problem.

The increase in complexity of mathematical models in an attempt to approximate reality and desire to have near real-time results have emphasized the need for fast numerical simulations. Especially in areas where classic numerical methods struggle to produce valid solutions in reasonable computational time due to their
complex behaviour on multiple temporal and spatial scales, such as (cardio-vascular) fluid modelling, machine learning techniques can be of help. The aim of this study is to construct a single reduced order model, based on neural networks, for time-dependent incompressible blood flow through the aorta that can account for varying velocity inlet conditions, material parameters and geometries (computational domains). The objectives are to minimize the reduction of accuracy of simulated time series with OpenFoam, and to obtain speedup compared to the OpenFoam simulations.

In this study, aortic blood flow during one heartbeat is modelled by Navier-Stokes equations for incompressible, Newtonian fluids. Data for training and testing the neural networks was generated using the finite volume method. The network architecture consists of a convolutional encoder and decoder model for dimensionality reduction, with an additional neural network for time evolution inserted between the encoder and decoder. The network takes one time step as input and predicts five consecutive time steps ahead. Three different networks for time evolution were tested. The best performing network was tested on increasingly complex computational domains. Thereafter, the network’s ability to generalize to varying inlet velocity patterns and new variations of the computational domain was tested, for which the network for time evolution was adapted to take into account varying inlet velocity patterns. The performance of the networks was evaluated on predicting one to five time steps ahead from one input time step, and using the prediction of one time step ahead recursively to obtain the prediction of one entire heartbeat.

The best performing architecture found was an encoder, recurrent neural network with long-short term memory units for time evolution, decoder model combination. The generalizability for the tested material parameter, blood viscosity, while keeping the inlet velocity pattern fixed, appeared quite good. A relative mean absolute error (MAE) of around 10% was obtained for straight, bent and bifurcated channel geometries. When testing the network on varying inlet velocity patterns, the relative MAE in the domain increased considerably to
around 25%. In general, the relative errors were significantly higher in comparison to the absolute errors, and mainly increased by low velocity parts of the domain and time series. In addition, the full height of the velocity peak was not always captured and a spike in the domain MAE was seen for rapidly decreasing inlet velocities. Also, the network was unable generalize to new geometries.

Various attempts to improve the accuracy, including altering the loss function and augmenting the data, were not successful. However, many choices of data augmentations, normalization techniques and loss functions were not tested and could improve the performance. The generalizability to different computational
domains could be improved by adding more geometries and more variation to the geometries in the data. Nonetheless, the prediction of one heartbeat was obtained in approximately 20s, which is equivalent to an achieved speedup of around 20 compared to OpenFoam simulations. In conclusion, this research should be seen as a basis for time-dependent blood flow predictions in the aorta, from which a multitude of different paths can be explored.

Currently, quantum computing is making large steps to becoming a mature technology. Many companies are developing their own quantum hardware for both research and preparing for practical deployment. The main challenges in the past years have been an abundance of practical applications for the few-qubit Noisy Intermediate-Scale Quantum (NISQ) quantum hardware and scaling the qubits and depth of the quantum hardware. For these reasons, quantum computing was not yet at the maturity level needed to create a useful application level quantumbenchmark. Many quantum benchmarks have been developed, but these either aim at qubit level assessment or are lacking in practical usability. For a benchmark to be useful, the practical application of the quantum hardware needs to be reflected. For this a practical application is required and this was not yet achievable with current quantum hardware scales. Benchmarks at the component level (individual qubits, quantum logic gates) have been developed widely and are useful for the development of the hardware. This is, however, more aimed at basic quantum research rather than application [21]. This also serves a fundamentally different goal than a performance measure of quantum computers. Many different forms of quantum hardware are being used, without a clear dominating implementation. Each of these have different dynamics and metrics, and can therefore not be generalized [97]. For this reason, making a benchmark for low-level hardware aspectswill not properly reflect its performance compared to other implementations of the quantum hardware. Furthermore, while benchmarks for single qubit operations have been developed [32, 36, 70, 102], these performances do not accurately reflect quantum operations on larger scales. Noise levels, for example, are an important metric in single-gate performance. The noise, however, varies per gate and due to qubit entanglement will propagate unpredictably throughout the system [38, 43, 97]. This makes it impossible to use single gate noise performance to extrapolate for the entire system, while for classical computers this would have been possible. These difficulties in determining the performance will require abstraction from the low level performance and an application level benchmark is needed to properly verify the performance.

This research investigates the possibility of solving one dimensional Poisson's equation on quantum computers using the Variational Quantum Linear Solver (VQLS) as a simplified test case for fluid dynamics applications. In this work, Poisson's equation is discretized with the finite element method and the resulting matrix is decomposed as a linear combination of unitaries to be cast in VQLS. When using Pauli Gates as a basis, the matrix is inefficiently decomposed with an exponential number of terms in the number of qubits. On the other hand, using gates with higher entanglement allowed for an efficient decomposition but requires high qubit interconnectivity. Numerical experiments were carried out on a quantum simulator: iterations to success were larger than the best classical counterpart and scaled exponentially for increasing qubits numbers. Across all the experiments performed, scalability was an issue mainly because of the vanishing of the gradient in the cost function

The chemical reactor network (CRN) approach is a practical tool for precisely predicting the species concentration in combustion processes with low computational cost. This work examines the capability of the emerging Julia programming language and its ecosystem in solving large CRNs. The packages DifferentialEquations.jl and ModelingToolkit.jl are employed to defining and solving stiff ordinary differential equations, for which the implicit time-integration methods Rodas5 and TRBDF2 with the GMRES linear solver are used. The graph structure of reactor networks is constructed by LightGraphs.jl and SimpleWeightedGraphs.jl. The differential equation solver and the graph data structure are connected via NetworkDynamics.jl. It is concluded that Julia is a competent tool for CRNs containing up to 1000 nodes each with 4 species. Julia is capable of simulating pollutant formation in large reactor networks with reasonable time and memory space.

In September 2018, the Smart Teddy project was founded by a group of researchers within the Hague University of Applied Sciences1 in the Netherlands. The Smart Teddy project is a multidisciplinary project aiming to create an interactive system, using a teddy bear as a focus point, which collects the data needed in order to enable seniors with dementia to live independently for a longer period of time. Over the last three years, three prototypes of the Smart Teddy have been developed. The Smart Teddy project was introduced as a final project for students following the BSc program Electrical Engineering at the Delft University of Technology. Starting in April 2021, a team of six students attempted to further develop the Smart Teddy over the course of 11 weeks. This thesis contains the Human Interaction & Integration subdomain of the Smart Teddy thesis project, where Human Interaction refers to the aspects of the Teddy that encourage interaction with the user, and Integration refers to the combination of all subdomains into one fully functioning prototype. In this thesis, the design choices, implementation methods and verification are discussed. The contribution to the prototype regarding Human Interaction & Integration are the addition of a movement system using pneumatics, the implementation of a flexible touch sensor, the ability for the Teddy to produce audio, to communicate wirelessly with the Base Station, and for all components in the Teddy to communicate with the main controller. The final prototype has been implemented using the Raspberry Pi Pico microcontroller, which was mounted on a custom PCB. All controls are provided by the Pico, and uses I2C, SPI, UART, and analog and digital inputs to communicate with the sensors and actuators. These sensors and actuators were implemented using off-the-shelf breakout boards and drivers, to allow for fast design and test iterations. The movement of the Teddy has been implemented using air pumps and molded silicon rubber, and the tail wagging is implemented using the same principle used for soft robotic grippers. The final prototype is fully functional and meets 16 of the 20 requirements - the requirement concerning speech recognition and the noise produced by the pumps have not been met.

The amount of people dealing with dementia is rising globally. The amount of caretakers is, however, not. Therefore, technological aids are needed to support people dealing with dementia and relieve the stress on their caretakers. Current solutions provide tracking of people with dementia. Also, different robots exist that provide people with companionship. However, no solution exists that combines tracking and companionship capabilities. Therefore, the Smart Teddy is introduced. The Smart Teddy can track different indicators that indicate the progress of dementia and simultaneously provide the user with companionship through interaction. The goal of this thesis is to design a data acquisition system that acquires meaningful data that can be used for the development of algorithms that will autonomously determine the progress of dementia. To achieve this, a system with a Teddy and a Base station has been designed. The Teddy has a sound-, a carbon monoxide-, a smoke- and a movement sensor. Also, a real-time module is implemented to be able to assign the current time to the measurement data. Lastly, a GPS and GSM module is implemented to be able to track seniors in case they wander. In the Base station, a mmWave sensor is implemented that tracks the position, velocity, and direction of the persons present in the room. Also, a processor is implemented that gathers and stores the data from the mmWave sensor and the data from the Teddy which is sent via a LoRa connection. In addition, the designed system can store the collected data for more than one week. The collected data can be used by an expert in dementia to extract meaningful information about dementia progress, after that, an expert in digital signal processing is needed to develop algorithms that estimate the quality of life of a senior suffering from dementia.

With the increasing demand in home-care service to provide early intervention at the homes of seniors suffering from early stage dementia, the Smart Teddy prototype offers a technological solution to disburden caregivers, to promote and track the health and conditions of the senior and to prolong their independent life at home. The Smart Teddy is a project founded in 2018 by a research team of the Hague University of Applied Sciences. It is an interactive, companion robot - disguised as a toy dog - that serves as a therapeutic promoter while simultaneously monitoring the quality of life of the senior with pre-determined indicators. It consists of a Teddy to provide the interaction with the user and a Base Station for data processing and charging of the mount-in battery of the Teddy. The Power Operations and Distribution group carried out research on and developed suitable solutions to supply power to the Teddy with rechargeable batteries, to integrate controlled wireless charging of the battery for user-friendliness and to provide a streamlined power distribution throughout the Smart Teddy’s system. Based on an iterated program of requirements and a power budget analysis on the set of installed electronics, a design is implemented for the power system of the Smart Teddy. A design sequence is followed consisting of four stages: (1) battery selection, (2) charger selection, (3) power conversion and distribution, and (4) safety and failure protection. A power system is developed for the Smart Teddy that is able to supply power with lithium-ion batteries with a battery life of at least 12 hours providing a battery capacity of 25.16 Wh. Thereafter, the installed batteries located in the Teddy can be charged wirelessly by placing the Teddy on the Base Station (a dog bed) to reinforce the less robot-like and a more natural look of the Teddy. Furthermore, this system ensures that all electronic modules with different operating voltages and current draws are provided with the necessary power specifications through power-sharing paths and the usage of power converters. Lastly, safety measures and failure protection methods are developed to ensure the safety of the user through the usage of fuses, switches and, cable and PCB management. The design has been verified using the appropriate verification methods where the program of requirements is used as a guideline and assessment tool. The Power Operations and Distribution is largely complying with the program of requirements and is performing according to the predetermined functionalities. Consequently, the power system of the Smart Teddy is integrated in a real, spatial prototype, namely in a toy dog (the Teddy) and its dog bed (the Base Station).

Markov chains are used to describe random processes in discrete time, which have the property of being memoryless. This report covers Markov chains on a finite space that are homogeneous in time and mainly follows the structure of ''Markov Chains and Mixing Times''. Markov chains exhibit a strong connection with electric networks. We exploit such a connection and apply the laws of physics to answer several probabilistic questions about random walks, which are certain types of Markov chains. This connection is then called the electric network approach and is built on translating the random walk into an electric network by relating the transition probability to the so-called conductance. The electric network approach provides problem simplification tools, such as the Series/Parallel Law, and powerful inequalities, such as the Nash-Williams inequality. These tools are based on physics and are often more intuitive than their probabilistic counterpart.

We simulate a two-dimensional random walk that starts at the center of a square and ''escapes'' if it reaches the perimeter of the square before returning to the center. We then compare this escape probability to an upper bound, which results from using the Nash-Williams inequality. The sharpness of the upper bound depends on the choice of edge-cutsets. We find that choosing edge-cutsets with a minimal amount of edges gives a sharper upper bound, than choosing edge-cutsets that contain all the edges of the square. The relation between the upper bound and the escape probability seems to be independent of the size of the square. Furthermore, we provide proofs that are not explicit in ''Markov Chains and Mixing Times'' and ''Reversible Markov Chains and Random Walks on Graphs'' and add to the contents of ''Markov Chains and Mixing Times'' by studying random walks from a graph theory perspective.

This thesis is devoted to option pricing on backward-looking rates. For the last decades, interest rate products were often linked to IBOR rates. IBORs are short-term borrowing rates charged between global banks in the unsecured interbank market. The purpose of this thesis is to compare the Hull-White model to the Black-Karasinski model for the pricing of caps/floors on compounded rates. Both models are so-called short-rate models, which are widely used for interest rate modelling. Due to the IBOR reform, new products are expected to appear in the market. One type of these products is caps/floors linked to the new Risk-Free Rate (RFR). The new RFRs will be in-arrears backward-looking rates and, as a consequence, have an impact on the choice of pricing models.
This thesis considers caps/floors on the new compounded RFR rates. For both models various pricing techniques for caps/floors on compounded rates are investigated. For the Hull-White model, the pricing kernel approach and a Monte Carlo simulation are explored. The pricing kernel approach yields an analytic formula for caps/floors on compounded rates. This formula is also used for the comparison. For the Black-Karasinski model, the pricing kernel approach, the trinomial tree method and the Monte Carlo simulation are considered. The pricing kernel approach yields a semi-analytic formula for caps/floors on compounded rates. However, in practice the computation time of this semi-analytic formula turned out to be substantial. Further, despite the fast computation time of the trinomial tree for LIBOR caps/floors, the trinomial tree method is rather slow for the caps/floors on compounded rates. As a result, the Monte Carlo simulation is the most suitable pricing technique, along the three
explored methods, for caps/floors on compounded rates under the Black-Karasinski model. Therefore, the Monte Carlo simulation is used for pricing caps on compounded rates in the model comparison.
Since there exists no liquid market yet for caps/floors linked to the new RFR, the models are calibrated to a proxy market. First, the Black-Karasinski model is calibrated to the proxy market using a heuristic approach. This heuristic approach is chosen as a compromise between computation time and accuracy. Then, the Hull-White model is calibrated to the Black-Karasinski model using the stripping method. Having both models calibrated, the price of caplets/floorlets on compounded rates are calculated. Thereafter, these prices are inverted to Bachelier implied volatilities for a uniform comparison. From the comparison of the two models, a difference in Bachelier implied volatility is observed in a range of 4 to 4 bps. This is of one order less than the volatility itself.

Complex mathematical models are used in computational neuroscience to stimulate brain activity to understand the biological processes involved. The simulation of such models is computationally costly, and thus highperformance
computing systems are selected as a potential solution to increase performance.
This thesis aims to implement a new versatile, multi-GPU eHH simulator (mgpuHH), explore its performance and make general observations on performance scalability over different modeling and cluster configuration properties. This work offers a multinode multi-GPU solution that offers excellent
scalability performance due to how the simulator is constructed, with the use of OpenMPI and CUDA. The simulator is configured with JSON configuration files, containing the neural descriptions and simulatorspecific settings. Consequently, enabling a userfriendly environment, for the neuroscientists, without the need of recompiling or understanding the source code. The gap junction calculations are identified as the critical function bottlenecking performance of the simulator. Therefore, an algorithm tailored to utilize GPU performance is implemented to decrease wallclock time for these specific calculations. For internode
communication, OpenMPI can be configured in two ways. Eiter share all possible compartments potentials with every node in the network or only share the compartments potentials to nodes that need them. These methods rely internally on MPI Allgather and Alltoallv respectively. When available, GPUDirect, NVlink, and RDMA are supported. The implementation hides communication overhead, when possible, by concurrently executable compute kernels. A neuron model from the Inferior Olivary Nucleus is selected for benchmarking. Reported results go up to 32 Nodes with a total of 64 GPU cards. The design shows linear weak and strong scaling within the experimental setups for intranode and internode scalability. With this simulator, networks over 10 million cells become available to model on largescale GPU clusters, setting a new standard for eHH simulations. Comparisons against related work on CPU and FPGAs have been conducted, a 100x speedup is achieved versus a single cpu threaded solution. Furthermore, a 2x speedup is achieved over an FPGA solution (flexHH) and 10 fold over a multithreaded CPU (GenEHH, with 128 threads) solution, both reported speedups are for a fully connected network with 7000 IO cells.

There exist a lot of methods to find the electromagnetic field behind a lens, so called the forward lens problem. In contrast very few methods can do the inverse, namely finding a lens that would produce a given image or light distribution for a known source. Here a solution to the forward problem, the Fraunhofer approximation, is used to find an approximate solution of the inverse problem using a neural network. Given an input image the network would predict the lens that can produce this image. In general this lens is not the classic convex/concave shape but is a freeform lens. The predicted image produced by the predicted lens can be computed by the Fraunhofer approximation. To train the network this predicted image is compared to the
desired image. This unsupervised training method is similar to that of Physics Informed Neural Networks (PINN), which is a recent approach to solve PDE’s.
The phase contour of the lens is represented by a B-spline curve. The control points of this spline are the output of the network. In this way very few output variables can be specified by the network to achieve a smooth detailed lens shape.
To give a proof of concept a one dimensional version of the Fraunhofer approximation is used. For this case the training already depends on many parameters. These are optimised for the lowest resulting loss.
The Fraunhoffer approximation limits the images that can be created. If the network, however, is trained on images that can definitely be created, it is able to almost exactly predict a lens that delivers the desired image.
The potential of the unsupervised training method in combination with a spline approximation should therefore be explored with other solutions of the forward problem. Namely a ray-tracing algorithm could be used, since this can create a wider variety of images. This would be computationally heavy compared to the
Fraunhofer approximation.

Increasing competition amongst airlines necessitates them to improve the efficiency of their operations. Even though maintenance, repair, and overhaul (MRO) represent a significant portion of an airline’s operational costs, aircraft maintenance scheduling is often still a manual process, producing suboptimal solutions. Airlines typically operate by congregating the bulk of the required maintenance tasks in extensive checks, called letter checks (A, B, C, or D). Letter checks require the aircraft to be taken out of operations and result in many tasks being executed before they are due, leading to more required maintenance over the aircraft's lifetime. The purpose of this study is to develop a methodology that provides flight routes to aircraft and plans the maintenance tasks individually within these routes over a given planning horizon with the objective of maximizing the utilization of the total remaining flying time of the fleet. To achieve this, tasks are planned as late as possible on overlays at a maintenance station, while being given a due date and a remaining number of legal flight hours that can be flown before execution is mandatory. For this purpose, we develop a mixed integer programming (MIP) model based on a city-day network representation. Because the computational burden of exact methods becomes too hefty for increasing problem sizes, several matheuristics have been developed to provide good solutions in quick fashion. The presented matheuristics either decompose the problem by aircraft or into time periods. The former constructs the flight routes and maintenance schedules aircraft per aircraft while the latter constructs them simultaneously in a rolling horizon fashion. For the rolling horizon matheuristics, several forecasting strategies have been designed as well. In an experimental study, one of the selected rolling horizon matheuristics was able to remove the need for aircraft to be taken out of operations for an A-check (the most frequently occurring letter-check), potentially saving up to \$ 7.2 million per aircraft over a time period of ten years. Furthermore, the lost flying time, incurred by planning maintenance tasks before they are due, was decreased by over 98\%, resulting in a higher utilization of the task intervals and less required maintenance over the aircraft's lifetime. Finally, the dissection of the A-check into its individual tasks led to a more phased maintenance schedule by attenuating the peaks in workload for the mechanics workforce. Our presented approach can be used by mid-sized airlines to optimize their maintenance schedules through increasing aircraft availability and reducing maintenance costs over the aircraft's lifetime.

Skin grafting is a common technique employed to treat patients after burn injuries. In contrast to the frequency and gravity of contractures following from skin grafts, the phenomenon itself is still poorly understood and subject of studies. The development of an accurate model of skin contractures will allow medical researchers to better understand the healing process compared to current in vitro experiments and thus enable the design of efficient and patient-specific treatments. In this work we provide a mathematical model able to capture both the mechanical and biological processes involved in skin graft healing. Two-dimensional morphoelastic equations are used to model the mechanics of contraction of skin during the healing process. A system of equations describing the cell components (myo-, fibroblasts, collagen density and signalling molecule) is solved separately to derive the forcing terms for the mechanical system. The finite element method with bilinear quadrilateral elements is used to solve the differential equations on a moving time-dependent domain. A flux corrected transport (FCT) algorithm is used to stabilize the biological equations, thus enforcing positivity of the constituents in the dermal layer and nonlinearities are treated using Picard iterations. Time stepping is performed by applying the Euler backward scheme for the mechanical system and the implicit midpoint rule for the biological system. The results are replicated using the IGA (Isogeometric Analysis) library G+Smo in C++. The results of the IGA implementation provide a solid basis for future algorithms using IGA.

The level-set (LS) method uses a signed-distance function to capture the interface in two-phase flows. Geometrical properties can be easily obtained, and merging and splitting of the interface are handled automatically by the LS method. However, it is not inherently volume conserving. Several methods found in literature that aim to solve this problem are discussed in this report, including the interface-correction level-set (ICLS) method. The ICLS method uses an additional advection step with a correction-velocity field to restore global volume loss/gain. We present the volume-of-fluid-based local interface-correction level-set (VOF-LICLS) method. This is an extension to the ICLS method that aims to restore volume locally. This is achieved by coupling the ICLS method with the VoF method. In each time step we evolve both the level-set function and the volume fraction function. The VoF advection is performed using a Lagrangian-Eulerian method on a dual mesh. From the advected LS field volume fractions are constructed and compared to the advected VoF field. This allows us to use local volume fluxes for the velocity field, instead of a global volume flux. The construction of the correction-velocity is performed with the use of an analytic equation and the local volume fluxes. The novel volume correction procedure is then executed iteratively. The level-set equation is discretized in space with a finite element approach. Instabilities occur for the standard Galerkin approach for pure advection equation, so the SUPG method is used in order to obtain stable solutions. The performance of the developed method in this thesis is compared with LS and ICLS for three different test cases. We report a significant improvement for local volume conservation, and we observe that VOF-LICLS yields more accurate interface positions.

Quantum computing is a new form of computational technology, which can potentially be used to solve certain problems faster than is possible using classical computers. For this reason, there is an industry drive to develop early quantum computing applications. In this thesis, an overview of quantum computing technologies is provided, along with a practical discussion of the Traveling Salesman Problem, making use of the D-Wave quantum annealer. Subsequently, the main objective of the thesis can be investigated, which is to
explore how quantum computing can be used to aid in solving structural optimization problems. Two methods are developed with which simple 2-dimensional truss systems can be optimized using the D-Wave quantum annealer. The methods aim to find the most lightweight choices for the truss cross-sectional areas while complying with material limit stress constraints. The first method directly casts such an optimization problem into a QUBO format. However, due to difficulties with formulating the stress constraint, this method was found to produce a trivial optimization problem. The second method attempts to symbolically solve a truss finite-element problem, using the resulting symbolic expressions to set up an optimization objective function. Although these objective functions are confirmed to work via classical brute-force analysis, the quantum annealer is shown to have difficulty finding the global optimum solution for truss systems with three or more elements. These results indicate that it is not currently beneficial to use quantum annealing for these structural optimization problems. Nevertheless, some improvements to the method for setting up the objective functions are suggested. The next generation of quantum annealers is expected to perform better for these practical applications, potentially becoming a useful tool in the engineering toolbox.