Scientific computing and applied mathematics enable the exploration of and, sometimes even, the simplification of complex systems through various optimized modeling and simulation methods. These fields create and utilize computational resources to do so. Many problems, however, are still unsolvable or very difficult to solve with current well-established methods – be it algorithms or computers. Quantum computers were theorized and are now being realized to extend computational abilities. Though commercially available and widely researched, quantum computers today are still more proof-of-concept than ”universally” applicable tools. A major part of the problem is these systems are riddled with noise, hence the phrase noisy intermediate scale quantum (NISQ) devices is commonly used to refer to current day devices. There are many approaches to mitigating the effects of noise in quantum systems from both hardware and software perspectives. This work focuses on optimizing the device hardware by combining aspects of two already well-explored systems – superconducting quantum integrated circuits and topological insulators.
The former are relatively easy to fabricate and have become one of the main focuses of today’s industry. The heart of superconducting quantum circuits is found in two circuit elements: the quantum bit (qubit) and the resonator. The qubit manages quantum information processing. The resonator is a simple inductor and capacitor (LC) in parallel and is a well understood classical circuit element. Resonators play a key role in this research. In contrast, topological quantum systems are incredibly difficult to fabricate. In theory, however, topological insulators promise a strong shield against noise across the device. By leveraging the simplicity and ease of simulating classical LC resonators and combining this with the noise-protection introduced in topological systems, this project lays the groundwork for developing a model supporting how such a hybrid hardware could process and protect quantum information. This thesis presents the characterization of how a two-dimensional array of LC resonators could behave similarly to a qubit when demonstrating edge modes, which are typically found in topological quantum systems. An approach for how to model such systems is proposed from the perspective of architecture, optimal control, and metrics.

As a response to the dry summer of 2018, Witteveen+Bos developed a model for water demand prediction to improve insight into water demands. Validation by water board "Hunze en Aas" has revealed the predictive power of the irrigation model to be very limited. For this thesis project, we developed a methodology for the detection of irrigation of crop parcels based on the radar vegetation index (RVI) derived from remote SAR images. This methodology can be used to improve the existing irrigation model.

To achieve this, we developed a novel model to describe the evolution of a vegetation index (such as RVI) during the growth season. Unlike existing models, the model presented in this thesis includes the effect of precipitation deficit, both as a temporary inhibitor of a vegetation index, and as a long-term influence on the crop growth. The model is non-linear in many of its model parameters. Therefore, heuristic calibration methods are unavoidable. We show that the standard calibration methods non-linear least squares and differential evolution are outperformed by a hybrid of both methods that we specifically designed for this application.

After calibrating the model to time series of 1167 potato parcels in the north-east of the Netherlands, we investigate different ways to cluster the model parameters. We propose explanations for three important clusterings through their RVI time series (speculative) environmental factors. Comparison with information on irrigated parcels for the years 2018-2020 reveals a statistically significant correlation between some of the clusters and irrigation. However, the variation in irrigation rate never exceeded a factor two. Therefore, no accurate classifier can be built based on these clusters.

We recommend two important ways to improve the current implementation. Firstly, the baseline RVI is consistently overestimated, resulting in mostly negative normalized RVI. Because of this, the model cannot properly describe precipitation deficit-driven fluctuations in the RVI. These fluctuations are an important part of system behaviour, so improving the estimation of the baseline RVI should be the first priority for future research.

Secondly, the exact irrigation dates of a set of parcels will be very useful. Comparing these dates to the corresponding RVI time series will make it possible to uncover features of the RVI evolution that are indicators of irrigation. The model parameterization can then be tuned to optimize sensitivity to these features.

Emission of ammonia and nitrogen oxides puts pressure on vulnerable ecosystems in The Netherlands. Satellite data from TROPOMI and CrIS gives vertical column density (VCD) maps for nitrogen dioxide and ammonia respectively. The Flux-Divergence method converts a VCD map to an emission map, by temporally averaging the divergence of the flux of the trace gas and estimating a sink term. This research proposes two improvements to the current implementation of the Flux-Divergence method at the KNMI for nitrogen dioxide. On the one hand, noise is reduced by computing the divergence before interpolating TROPOMI data to a regular grid. On the other hand, some emission locations are enhanced by reducing divergence in the wind field. An algorithm is provided to reduce this divergence. This thesis also explores the sensitivities of the method to different choices in its implementation. Finally, this research implements the Flux-Divergence method for ammonia. The thesis shows that, for ammonia, the method depends strongly on the estimation of the sink term, as the flux-divergence map is not able to capture homogeneous, spread-out emission sources.

The need for accurate estimation of hydrodynamic and water quality model variables arises from the UNITED project, which aims to create high-resolutional forecasting systems for monitoring the cultivation of seaweed and flat oysters and operating of the Belgian pilot of UNITED in the coastal area of the North Sea. Accurate observations of physical variables are usually only known for small domains of the model, on the water surface. Therefore, data assimilation is applied on different hydrodynamic models to search for improved estimates of waterlevel, water velocity and temperature. The sequential data assimilation algorithm, the Ensemble Kalman filter is considered. The algorithm is a Monte-Carlo approximation of the Kalman filter, both using accurate observations assimilated into the model, where the model each time is shifted towards the observations when available, providing an optimal trade-off estimation between the model estimations and observations. Two models are considered: a 1D model of the Western Scheldt estuary in Python and the 2D model with depth of the Western Scheldt estuary implemented with software packages Delft3D FM and OpenDA. Model estimates and estimates of model with assimilated observations are investigated in various experiments to look for improved predictions, using twin experiments to generate artificial observations over the whole domain. The various experiments contained the search for the effect of assimilation location on the estimates, of the effect of assimilation of different physical parameters, the effect of the observational error covariance and the effect of water surface assimilation on the estimation within the water column. In most cases, the Ensemble Kalman filter improved the estimate of waterlevel and water velocity with varying results up to a decrease in rmse of a factor four, while the assimilation of temperature gave a worse prediction. Furthermore, assimilation of waterlevel gave the best improvement in estimate. For the investigated models, assimilation of observations near the boundary conditions with implied noise gave the most improved estimates. Furthermore, assimilation of water surface observations improved the estimate within the water column for water velocity with a factor of 2, while temperature assimilation did not show any improvement. The result for temperature may be due to a collapsing Ensemble Kalman filter due to small standard deviations and a not realistic model setup for temperature. Therefore, assimilation of only observations at the surface may be used to accurately improves water column estimations for water velocity. For temperature, more research is needed. Advised is an experiment with a different model setup with more realistic and longer spin-up time of temperature. The collapsing Ensemble Kalman filter can be prevented by initialization of new ensembles before the the collapse happens. In further research, data assimilation can be applied on the DCSM model, a model involving the area of the Belgian pilot.

Ammonia (NH3) is an important chemical compound in the nitrogen cycle. Ammonia is an essential nutrient and an important part of fertilizer, which in soil leads to increased growth of crops. However, the current excess of NH3 emissions is a hazard to environmental and human health. While ammonia
emissions need to be reduced, the emission estimates are still highly uncertain.
In this study, a method is developed to combine the chemical transport model LOTOS-EUROS with measured ammonia concentrations to improve the ammonia emission estimates in the Netherlands and the surrounding regions. The measurements used are generated by the miniDOAS instruments on LML stations and the IRS instrument on board the future MTG-S satellite. The proposed method is an adjoint-free 4DVar method. The 4DVar method aims to retrieve the emission parameters for which the LOTOS-EUROS model determines NH3 concentrations that resemble the measurements while keeping the emissions fairly similar to the original inventories. A linear approximate model has been developed, which uses the near-linearity of the NH3 concentrations in terms
of the NH3 emissions. When using the approximate model, the 4DVar
method can be solved without using an adjoint model, making the method adjoint-free. Subsequently, the 4DVar cost function is rewritten to allow the emission parameters to have a lognormal prior distribution. A maximum likelihood approach is developed to estimate the parameters of both the prior distribution of the emissions and the likelihood of the measured observations. Last, a preconditioner in reduced space has been considered, to estimate emissions on a fine spatial resolution, while keeping the computational cost
feasible. This preconditioner uses the property that the emission parameters are correlated in space. First, the methodology has been tested in an identical twin experiment where the emissions vary only in time and strength, using the LML observations. It was concluded that the methodology worked well
for short periods (less than 30 days), but the results were dominated by observational noise. When using the real observations in the 4DVar
method, the results seem unrealistic Second, the method has been tested in an identical twin experiment where emissions vary in space, as well as in time and strength. Here, synthetic IRS observations of the future MTG-S satellite are
used. The optimized emissions did resemble the true emissions of the twin experiment. Observational noise appeared to no longer be an issue. However, the results were not perfect. The regions with the highest emission increase appeared to be underestimated, low emission areas appeared to have large
relative estimation errors, and estimates for coastal regions seemed to be incorrect. Hence, on a local scale, the emission estimates can be imperfect, but overall the adjoint-free 4DVar method does greatly improve the emission inventories.

In light of our depleting fossil fuel reserves and the relatively `cheap' extraction of oil and in spite of the highly nonlinear nature of reservoirs, waterflooding has become big business. In recent times, the use of numerical reservoir simulation has not only become possible but has increasingly been used in the petroleum industry in the forecasting of output and money to be made. However, this numerical modelling and automated history matching is not without its problems. The inner workings of sophisticated commercial reservoir simulators are often taken for granted, i.e., ``black boxes''. These simulators are constructed around a numerical method, with its advantages and disadvantages. Herein, the input settings play a role in the stability and precision of results. For example, the chosen iteration method, grid spacing and time step size or even the choice of iteration parameters, all based on insufficient data, leads simulators to be unreliable and inefficient. Moreover, even under the assumption that such ``black boxes'' are able to produce a true prediction, this is entirely conditional on correctly establishing the current state and conditions. Thus, practitioners have many global settings given, many of which inaccurate. These many uncertainties can lead to costly mistakes.
The aim of this study therefore: is to develop a tool that can quantify the uncertainty of a core flood model and a parameter estimation routine.
Specifically, it investigates whether, given limited incoming data, an uncertain parameter can be estimated and then used to simulate and quantify the uncertainty of the water saturation and oil pressure in the core sample. In this context, we question if it be used to provide a history match of the core sample.
To see how the uncertain input parameters are reflected in a model output, the tool, based on, the IMPES scheme simulates the two-phase flow, and the Ensemble Kalman filter (EnKF) to estimate the parameters. Building on the base twin experiment, a variety of twin experiments were performed to understand the parameter estimation, by presenting and visualizing the uncertainties in the data and states. We investigate the use of the EnKF for history matching and ways to improve are also explored.
Based on the results of this study, it is concluded that the Ensemble Kalman Filter is capable of effective parameter estimation. With modification, it can also be used for history matching and uncertainty quantification. It clearly suggests that the utility of numerical modelling and automated history matching will continue to make contributions to the success of the exploration and extraction of fossil hydrocarbons.

In this thesis, sensitivity analysis is used to study the influences of parameters on specific outputs in the hydrodynamic model 3D DCSM-FM of the North Sea. The sensitivity analysis is the study of how uncertainty in the outputs of a model can be divided and allocated to different sources of uncertainty in its inputs. The software Delft3D FM is used to simulate the model, which is developed by Deltares. This thesis is supported by German pilot of the UNITED project, which studies the possibilities of combing blue mussel and sugar kelp cultivation with wind energy. The investigation is conducted at FINO3 platform, 80 km off Sylt.

In this thesis project, temperature and current velocity are selected as outputs in sensitivity analysis, which are influential factors of blue mussel and sugar kelp growth. Specific parameters in the hydrodynamic model are selected as inputs respectively. Three sensitivity methods are conducted: Morris, copula-based and variance-based method. Among them, copula-based and variance-based consider the independency information, while parameters are assumed dependent in Morris method. To generate samples, parameters are transformed into a unit hypercube in Morris method and run on the contour of the grid cell, composing paths. Between two steps within the paths, only one parameter changes at a time (OAT method). The input domain is scanned with a better strategy to separate the paths maximizing the dispersion. Each parameter’s elementary effects are calculated within paths, evaluating the changes in outputs contributed by the single parameter. Then (absolute) mean and variance of elementary effects are used as sensitivity indices. Copula-based method uses similar sampling and the same measurements, but it gathers parameters into copulas before sampling to include the dependency information. In variance-based method, the variance of the outputs’ conditional expectations is used to measure the sensitivity. Only random samples are needed in this method.

Morris and copula-based method prove the temporal and spatial similarities of parameters’ sensitivity behavior. Convective and evaporative heat flux are the most influential parameters of temperature, and they also show correlations with other parameters. Air density influences current velocity the most, while Smagorinsky factor is the most correlated parameter of current velocity. Variance-based method gives similar results about rankings of influences. Correlations are proved to exist among parameters. Uniform horizontal eddy viscosity/viscosity in definition files have no impacts, as they are overwritten. Three methods are compared. Except the differences in independency, sampling and measurement, there are some other differences. Much more samples are required in variance-based method and it is used mainly to decide the existence of significant correlations and whether a parameter can be neglected. While Morris and copula-based method ranks the influences and correlations.

Al ruim een half jaar houdt het de hele wereld in zijn greep: het Corona virus. Waar we dachten dat het allemaal begon als een onschuldige griep, werd al snel duidelijk dat er meer aan de hand was. Wuhan kampte al een tijdje met dit onbekende virus en op 23 januari 2020 werd het zelfs zo serieus dat de Chineese overheid een lockdown afkondigde voor Wuhan en andere steden in de provincie Hubei. Winkels, openbare plekken en -vervoersmiddelen werden gesloten, kinderen zouden vanuit huis geschoold gaan worden en waar mogelijk werd opgedragen thuis te werken. Zoiets hadden we nog nooit meegemaakt.Toch leek dit voor menig Nederlander één grote ver-van-mijn-bed-show, tot het nieuws ons bereikte dat ook in Italië besmettingsgevallen van het COVID-19virus werden geconstateerd. Langzaam maar zeker kroop het virus verder naar ons kikkerlandje en op 23 maart 2020 was ook in Nederland het virus zo serieus aanwezig dat een lockdown werd aangekondigd. Nu, zo’n 4 maanden verder, weten we niet meer beter. Iedereen is in bezit van één of meerdere mondkapjes, op het verplichte gebruik van een winkelkar in de supermarkten wordt niet meer gemopperd en anderhalve-meter-samenleving maakt grote kans om de Woord van het Jaar-verkiezing 2020 te winnen.Toch blijft iedereen het spannend vinden hoe deze crisis zal aflopen. De voortgang van en nieuwe informatie over het virus zijn al tijden hot topic op social media en bijna dagelijks verschijnen er nieuwe wiskundige modellen met aanvullende informatie in de krant. Deze modellen geven ontzettend veel informatie over onder andere de verspreiding en het verloop van het Corona virus. In dit verslag bekijken we met statistische methoden hoe we ziektes kunnen voorspellen. Daarnaast gebruiken we een methode om voorspellingen met data te combineren. Dankzij het RIVM zijn er veel gegevens over de huidige Corona situatie beschikbaar. We gebruiken deze data om het verloop van het virus te modelleren, rekening houdend met een modelfout en een meetfout. Hiermee brengen we in kaart hoe het virus zich de afgelopen tijd heeft gedragen en wat we in de toekomst kunnen verwachten van een vergelijkbare ziekte. Alle berekeningen en plots die zijn gebruikt, zijn gemaakt in Rstudio, een statistisch computerprogramma.

The graduation project was conducted at the CFD department of Nuclear Research And Consultancy Group (NRG) in Petten. The modeling and simulation of Taylor bubble flow using CFD can contribute significantly to the topic of nuclear reactor safety and in particular, in the emergency cooling of nuclear reactors during a loss of coolant accident, or in the U-tubes of a stream generator during a pipe rupture. To achieve an accurate representation of the gas-liquid interface for high values of Reynolds number, a general interfacial turbulence model should be developed which adapts to local conditions automatically. Direct Numerical Simulation (DNS) of relevant large interface two-phase turbulence has the potential to contribute to this, as it can produce more refined insight while being complementary to experimental data. The current graduation project illustrates a simulation approach towards DNS of turbulent co/countercurrent Taylor bubble flow. It comprises a continuation of the novel simulation strategy indicated by (Frederix et al., 2020) in which LES of co-current turbulent Taylor bubble flow using OpenFOAM were indicated and the authors concluded that LES mesh resolution is not sufficient to capture accurately the gas-liquid interface, velocity fluctuations, and bubble disintegration rate. To counter this, in the current work, a Basilisk code is developed which due to its adaptive local grid refinement and its accurate solution of advection equation, comprises a better choice than OpenFOAM for DNS in two-phase flows (via the settings of (Hysing et al., 2009) for laminar bubble flow and (Shemer et al., 2007) for turbulent co-current flow) since it captures sharper the interface and reduces the computational cost significantly. Except for OpenFOAM, Basilisk is also successfully validated against ANSYS (Araujo et al., 2012) for the laminar Taylor bubble flow. Last but not least, the work is further extended to the simulation of laminar and turbulent counter-current Taylor bubble flows in which the effect of the choice of the pipe diameter and the initial bubble length on the bubble’s decay rate is analyzed for the experimental setting of (Mikuz et al., 2019). Overall, despite the lack of fully DNS quality, this study extends the work of (Frederix et al., 2020) and provides further insight into the performance of Basilisk in two-phase flows at a reasonable computational cost. The results and conclusions from the current study may contribute to the development of low-order turbulence models and the validation of more general two-phase modeling strategies.

This study aims to improve estimates of NOx emission strengths by assimilation of TROPOMI satellite retrievals in the LOTOS-EUROS chemical transport model. Nitrogen oxides (NO and NO2) play a pivotal role in atmospheric chemistry, are an important source of air pollution and contribute to nitrogen deposition over vulnerable natural areas. Therefore, it is paramount to have accurate estimates of emissions. Emissions are parameterised by multiplicative correction factors for NOx emission strengths from existing inventories. Optimal estimates of the correction factors are calculated by assimilation of TROPOMI NO2 retrievals in LOTOS-EUROS. This study proposes an adjoint-free approach to solving the 4DVAR data assimilation problem. Due to the near linearity of LOTOS-EUROS with respect to NO2, an approximate model is proposed that calculates NO2 concentrations from the background state and a linear combination of the influences of the parameters on the state. This approximate model is calculated from an ensemble of LOTOS-EUROS simulations with perturbed parameters. After substitution of the approximate model in the 4DVAR cost function, it is quadratic and the minimum can be calculated directly. For this approximate cost function, the optimal estimate of the parameters and the covariance of this estimation can be obtained with negligible computational costs. Twin experiments, where synthetic satellite observations are assimilated, show that the adjoint-free 4DVAR method is able to accurately minimise the cost function. Errors in estimated parameters are in agreement with the covariance calculated for the estimate. It was also shown that by using domain decomposition, it is possible to generate the approximate model from fewer simulations of LOTOS-EUROS and thereby increasing the computational efficiency of the method. In experiments using TROPOMI NO2 retrievals, the method performs well when modelled plumes align with the retrievals. However, differences between modelled plumes and retrievals, that are resolved by the high resolution of the TROPOMI instrument, may strongly hamper results as the method is only able to correct the intensity of the plumes but not their positions. This leads to an underestimation of NOx emission strengths. Further research is required to handle differences of plume positions in LOTOS-EUROS and TROPOMI retrievals to apply the method to actual TROPOMI retrievals. In addition, more research into domain decomposition may further increase computational efficiency of the method.

Although a transition to more sustainable energy production is necessary, fossil fuels will remain a crucial contributor to the world's energy production in the near future. In numerically maximizing the production of these fuels, as well as in many other optimization problems, an objective function has to be optimized on the basis of an input vector, related through some underlying model. Although the adjoint methodology generally allows for efficient gradient-based optimization of such a problem, it quickly becomes infeasible when the model comprises a large-scale system, or access to this model is prohibited. To resolve this, we consider the application of a model order reduction scheme, in combination with subdomain surrogate modeling, to perform the optimization using a reduced-order approximation of the model. In particular, we employ principal orthogonal decomposition (POD), efficiently reducing the size of the underlying system of equations, on the basis of a limited number of samples of the full-order model. Applying a domain decomposition, this number of samples can be reduced even further, although at a decreased efficiency. Next, radial basis function (RBF) interpolation is applied, using the samples to construct a trajectory piecewise linear approximation of the reduced-order model in each subdomain. Combining these different techniques, an optimization algorithm is constructed, applying the adjoint methodology to the reduced-order model in order to compute an approximate gradient. The accuracy of this approximation was found to be poor, but comparable to alternative sample-based methods.
An improved accuracy could be achieved by reducing the number of input parameters, allowing for more efficient optimization when applying the algorithm to a particular reservoir model. For another model, however, the algorithm performed worse upon reducing the size of the input, as a result of the fewer degrees of freedom in the optimization procedure. Reacquiring this freedom during the optimization, improved results could be attained, but the number of iterations and thus the cost of the method increased drastically. Comparing the full input implementation to another sample-based method, specifically a straight gradient ensemble algorithm, it was found to produce comparable results. Each method was able to surpass the other, dependent on the particular situation, though the reduced-adjoint algorithm generally expended more effort to attain similar results. This suggests that further study is necessary, for example improving the RBF interpolation or input reduction techniques, to fully exploit the benefits of the POD-TPWL methodology.

In this thesis a deterministic wave model is used to reconstruct and predict the sea surface motion from FMCW (Frequency Modulated Continuous Wave) radar data, produced by Radac. The deterministic model that is used to do this is based on the linear wave theory. The radar is looking horizontally straight towards the waves in 5 separate beam directions of -40,-20,0, 20 and 40 degrees. Using the FMCW principle the backscatterd signal is converted into velocity and spatial range information. After some compensations (current for example) this velocity data can be treated as horizontal component of the orbital velocity of the wave. By using a least-squares solving approach (the trust-region reflective algorithm) on these orbital velocities and the expression that holds for them in the linear wave theory the model can be fitted to the measurements. The result of the least squares solver consists of a set of parameters for wave amplitude, phase and frequency. With these parameters the deterministic motion of the sea surface can be computed. This method is tested using artificial data and a generalized one directional case (using information from 1 beam under assumption of infinitely long-crested waves). For the experiments with artificial data consisting of waves with Hs = 2 meters (significant waveheight) the results are promising. A prediction time of 30 seconds over a range of 150 meters with an average error of 15 cm in the one directional model (fitted on 10 second data over 384 meters) can be achieved. For the multi directional model this lies between 20 and 30 seconds with an average error of 25 cm, depending on the spreading of the waves. Experiments with real data show less impressive results, an accurate reconstruction of the surface can be given, but the predictive capability is very limited.

When building a convolutional neural network, many design choices have to be made. In the case of Deepfake detection, there is no readily implementable recipe that guides these choices. This research aims to work towards understanding the effects of design choices in the case of Deepfake detection, using the Python library Keras and publicly available datasets. The choices analysed are dataset composition, preprocessing, dropout rate, batch size, network architecture, and specific dataset. We also analyse the difference between training a network on original images and DCT-residuals of images. Lastly, we analyse the networks' generalisation and robustness capabilities. The goal of these experiments is to work towards a readily implementable recipe for Deepfake detection algorithms. Furthermore, this research provides an overview of image manipulation algorithms, an overview of recent research into convolutional networks, and an extensive overview of the Deepfake detection research field. To analyse dataset composition, we used different subsets of FaceForensics++, with different numbers of frames per video. We trained a shallow network, containing only four convolutional layers, on all three datasets. The dataset with one frame per video was the only one that did not result in immediate overfitting, although it contained less than two thousand frames in total. We continued with the small dataset and tested different preprocessing settings and dropout rates on our shallow network. We found that preprocessing and dropout were not able to increase the maximum achievable accuracy, although they were able to curtail overfitting. It is possible that accuracy did not increase due to the high variety of artefacts in FaceForensics++. Batch size also does not have any effect on the maximum achievable accuracy. However, the runtime required for training a network increases considerably as the batch size decreases. We tested DenseNet-121, Inception-v3, ResNet-152, VGG16, VGG19, Xception, and our shallow network on three different datasets: FaceForensics++, Celeb-df, and DeeperForensics-1.0. The goal of this experiment was to find what type of network is most suited for detecting Deepfakes with publicly available datasets of small size but high variation. We also wanted to see if there were differences in performance achieved on the different datasets. Although all networks except the shallow one were pretrained on ImageNet, three of the different networks tested immediately overfitted on all three datasets used: DenseNet-121, Inception-v3, and XceptionNet. The other networks encountered most difficulties with Celeb-df, on which none of the networks managed to reach 70% accuracy before overfitting. The easiest network to train on was DeeperForensics-1.0, on which our shallow network achieved 92.5% accuracy. However, when testing the networks' robustness, none of the networks trained on DeeperForensics-1.0 reached an accuracy higher than random on Celeb-df or FaceForensics-1.0. Shallow networks might be better suited for Deepfake detection on our small dataset. The shallow model and VGG16 achieved the highest accuracies. VGG19's performance is close to VGG16's. However, ResNet-152 is the deepest network used in this research and performs better than the shallower DenseNet, Inception-v3, and Xception. Lastly, training our networks on DCT-residuals was supposed to help our network focus on statistical image content rather than semantical image content. However, performance on DCT-residuals was at best similar to performance on original images. Our suggestions for continuation of this research are to experiment with different input sizes and other types of residual filters, collect larger (and higher quality) datasets with high variety, and to use interframe detection.

Combating air pollution has proven to be a difficult task for countries with rapidly developing economies. Poor air quality can be hazardous to people doing any outdoor activities. So being able to make accurate, short term air quality predictions can be very useful. However, making these predictions has proven to be quite difficult, since there are a lot of different physical and chemical processes involved in the emission and transport of the various aerosols that contribute to air pollution. So instead of the more traditional Chemical Transport Models (CTMs) we will be using neural networks in order to make predictions of one of these aerosols, PM2.5. In particular, we will be using a Long Short Term Memory (LSTM) network. In addition, we will include the simulations results from a CTM, LOTOS-EUROS, as input data to the LSTM network to improve the performance of the neural network. One of the main drawbacks of the LSTM approach is that whenever the PM2.5 concentration changes a lot, the predictions made by the LSTM network take some time to change as well, causing a visible time delay when looking at the measurements and predictions in the same time series plot. We will also try a simpler type of neural network, a Feedforward Neural Network (FNN) and compare its performance to that of LSTM. We found that using the simulation data does indeed improve the LSTM network. Not only in terms of the loss function used by the neural network and, but in particular in the amount gross overestimations by the network, which we use to quantify the LSTM time delay problem. We also found that FNN outperforms the LSTM approach, in particular on samples of high PM2.5 concentrations, which we argue is primarily caused by a low amount of samples in our dataset.

This thesis provides insights into the relation betwen two vital elements within the physical precipitation system: cloud top temperature (CTT) and precipitation. It investigates gauge data from ground stations in Germany and satellite data on CTT, targeted at the same stations in Germany. Cloud and rainfall characteristics
are considered and both simple and advanced mathematical tools are covered.
Statistical methods show that the data present is not stationary. Stationary data is required for applying time series analysis, either in the time or frequency domain. The key step in this research is dividing the big dataset into smaller subsets based on the provided characteristics: elevation, region and time. For these subsets the Pearson correlation and Spearman’s rank correlation coefficient show that significant correlations can be found. Lastly, this thesis looks into the possibilities for setting thresholds for cloud top temperature in
relation to the precipitation. These thresholds should be able to tell whether a day can be considered ’dry’ or ’wet’. Due to the incoherent data, these thresholds are not very optimal. Many circumstances need to be considered in order to make these thresholds fit specific situations.

Sailing against the wind follows a zig-zag trajectory. To find the optimal time and path-trajectory to move from one target to another during a race, this study analyzes how the wind determines the optimal time-path of Lasers, one of the smallest sailboats that compete during the summer Olympic Games.
To answer this question, this study uses four wind models in an algorithm developed in MATLAB to find the optimal time-path. The wind models were forecasts and wind measurements for the area of race R1 from the World Cup Series 2018 at Hyères, France. One of the wind models used were a Weather Research and Forecasting model (WRF) with a grid resolution of 1km, a time step of 10 minutes. On the other hand, the most basic model was a constant and uniform wind field.  The race R1 has three lines, limited by two buoys, and one point(buoy), one line and one point define a leg. R1 has five legs and two of them are against the wind. The results, time and path-trajectories, of each of the wind models, were compared with the results of the top 10 winners of the race. They showed that the legs sailed against the wind are also characterized by the location of the sailboats on the start line. The times of these legs using the WRF wind model and the race-time had an error of less than 5%. For the prediction of the start location, it was the same as the winner of the race. However, the direction of the paths was not predicted accurately for these legs. Using the constant and uniform wind scenario, the percentage error of the race-time respect to the winner is about 7%. However, the direction of leg 2 is not even similar to the winner. To review the effects of the heights of the waves this study proposes to model the sailboat in 3-dimensions including the X-coordinate of the sail-man position. In addition, a 3D model allows the analysis of how the center of effort (CE) on the sail is affected by the current and waves.

Reliable and efficient modelling of magnetic hysteresis in inhomogeneous and aniso-tropic media is an important step in developing a state-of-the-art closed-loop degaussing system for naval ships and submarines, to be developed by TNO and to be used by the Royal Netherlands Navy in an updated generation of naval vessels and submarines. Different models have been proposed to describe the nonlinear and history-dependent nature of ferromagnetic hysteresis at a material level. With a focus on three key differing aspects of models, namely linear versus nonlinear(hysteresis), isotropic versus anisotropic and homogeneous versus inhomogeneous, we attempt to discriminate between the performance of models on the basis of these criteria. More specifically, with increasing model complexity, we have combined Maxwell's equations with four different hysteresis models within the context of a prolate steel ellipsoid, whose ferromagnetic properties evolve under the influence of a uniform applied background field. Among other aspects, the hysteresis models differ in terms of physical motivation, complexity and parameter spaces. In this research, we have analysed four hysteresis models in more detail: The Induced - Permanent magnetization model, The Rayleigh} model, the Jiles-Atherton model and an Energy-Variational model, based on energy balances. The thus derived forward models have subsequently been inverted in order to estimate material hysteresis parameters. With increasing complexity also, twin experiments have been performed. This increasing complexity \textit{temporally} stems from the fact that the hysteresis models named previously, are stated in increasing order of complexity, and can all be modified in order to model anisotropic material by generalizing model parameters to tensors. Spatially, the increase in complexity is caused by the fact that in special cases, namely of uniform ellipsoid magnetization, an analytical formula relating the magnetic field, the background field and the ellipsoid magnetization exists by solving the Poisson partial differential equation on an infinite domain using direct computation with Green's functions.

Even though negative effects on the use of crude oil have surfaced over the past years, our energy matrix still largely relies on this energy source. The production of oil, therefore, plays an important role in our society. Unfortunately, the process of oil production is highly uncertain. There are uncertainties associated on the production strategy, e.g. where and how many wells should be drilled and how these wells should operate because of the uncertainties associated with the limited knowledge about the subsurface. In this thesis we are dealing with the uncertainty of the rock permeability distribution. Typically, rock permeabilities in the rock vary, but from the outside this can’t be perceived. If these rock permeabilities are estimated inaccurately, they will result in inaccurate pressure solutions. Then, this can lead to faulty decisions regarding the oil exploitation. To resolve this issue, a data assimilation technique may be applied to correct these model parameters based on mismatch of simulated data and observations. For this optimization technique, often gradient information is required. Since
in reservoir simulation the number of parameters generally is extremely high, computation of this information is computationally expensive. Therefore, a multiscale framework is employed to improve the
computational efficiency of the forward simulation. Multiscale methods are able to solve the model equations at a computationally efficient coarse scale and can easily interpolate this solution to the fine
scale resolution. Next, we use a Lagrangian set-up together with a multiscale framework to re-derive an efficient formulation for the derivative computation. However, as the multiscale method is prone to errors, this derivative computation formulation is recast in an iterative fashion, using a residual based
iterative multiscale method to provide control of these errors. In this thesis we show that this method generates accurate gradients. In contract to the high accuracy of the method, this method comprises a computationally heavy smoothing step. This issue can be resolved by making smart use of the Lagrange
multipliers, to re-derive an efficient iterative multiscale solution strategy. The multipliers are used to identify important domains of the region for which smoothing is required and for which regions we may neglect the smoothing. We show that the newly proposed iterative multiscale goal oriented method is computationally more efficient and we show that method is promising for efficient derivative computation, but that more work is required to fully demonstrate the benefit of this method.

Predicting the behavior of turbulent flows and how thermochemical properties develop such as temperature, enthalpy or concentrations is an import aspect in various fields. However, numerical calculations have a high time complexity. Therefore, models were constructed to approximate these flows. This thesis focuses on using probability density functions (pdf) to predict scalar probabilities in these flows. Since the pdf does not contain spatial information, small scaled mixing has a closure problem and has to be modeled using micromixing. A micromixing model, called the Shadow Position Mixing Model (SPMM) was introduced previously to calculate this mixing. In this project, its performance is determined for the mixing in two different flows. The model shows promising results for mixing of two passive scalar, initially mainly in one of three states. Comparing the results of various mixing models to the provided DNS, the SPMM predicts the evolution of the pdf over time adequately, but still has visible differences compared to the DNS. In the second test, the model is tested using an imposed mean scalar gradient in order to check the convergence of the mixing model. The SPMM does show promising results, but can not reliably predict a correct statistically stationary state. This is due to the fact that varying number of scalars and particles lead to significant inconsistencies. Under the current conditions, the SPMM cannot be reliably applied to flows with such an additional scalar force. The SPMM uses a near-neighbor sorting algorithm which has a high algorithmic complexity. For practical purposes, a lower complexity algorithm has to be developed in order to use this model for high number of particles.

The growing amount of plastic pollution in the oceans is worldwide a huge problem. There is an increasing amount of projects that try to clean up this pollution. To remove the pollution efficiently, it is useful to know how plastic litter moves, degrades and sinks. Models are being developed that can describe what happens with plastic in the ocean.

To model the behaviour of plastic in the ocean a lot of parameters need to be taken into account. The transport of plastic particles is largely determined by processes like the wind and the current but their movement also has a random character due to dispersion. Due to this random movement, the future position of a particle can be described by a probability distribution. To find that probability distribution, the Kolmogorov forward equation (or Fokker-Planck equation), in this context the same as the advection-diffusion equation, needs to be solved.

It is also possible that the plastic particles sink and settle on the bottom of the ocean. One goal of this project was to incorporate the settling of particles as an extra term into the advection-diffusion equation.

Forward models are used to predict where particles will go to. It can also be useful to have reverse time models that can describe where particles had their origin. To make reverse time models, it is necessary to solve a reverse time advection-diffusion equation. The main goal of this project was to derive and solve the reverse time advection-diffusion equation that includes the settling of particles. This is done by finding the adjoint of the Kolmogorov forward equation and the settling term.