This thesis investigates signal propagation and stability in spider web-like networks, focusing on how velocity differences, structural geometry, and complexity influence network behavior. Spider webs, known for their resilience, flexibility, and efficient vibration transmission, offer valuable insights into designing robust artificial networks. By employing mathematical and physical modeling, this study explores force distribution, signal propagation dynamics, and collision phenomena within these networks.

The study introduces distinct propagation approaches, ranging from simple discrete collision analysis to advanced continuous simulations incorporating energy dissipation, adaptive weighting, and refined collision detection algorithms. Key methodologies include simulations of force distribution using recurrence relations, random walk models, and wavefront propagation models to examine how signals traverse complex network topologies. These simulations reveal that network topology significantly impacts signal efficiency, propagation speed, collision frequency, and signal loss, with central nodes emerging as critical hubs of activity and congestion. Additionally, structural defects such as inactive nodes, altered masses, and weakened edges are systematically introduced to evaluate their influence on the overall stability and signal propagation efficiency. These imperfections profoundly affect network performance, demonstrating the necessity for structural adaptability and redundancy to maintain integrity under stress.

This thesis studies the evolution of N-body Keplerian systems (N=500) using an algorithm developed by P.M. Visser that mathematically predicts when a close encounter occurs.

The long-term simulation of planetary systems poses significant challenges due to the inherently chaotic and non-integrable nature of gravitational interactions in the N-body problem. This thesis examines the Wisdom–Holman symplectic integration scheme, a method specifically designed for nearly integrable systems. This scheme separates the dominant Keplerian motion from weaker perturbative forces, enabling stable integration over astronomical timescales. Emphasis is placed on understanding the practical limitations and capabilities of this method when using large time steps, particularly in the presence of mean-motion resonances and step-size resonances. Through extensive numerical experiments using the Rebound simulation package, the scaling behavior of integration errors is characterized, revealing a transition from secondorder to lower-order error regimes at large time steps. This shows that in certain systems, time steps significantly larger than the shortest orbital period can still yield acceptable accuracy. However, in systems with mean-motion resonance, strong sensitivity to step-size resonances is observed, requiring careful step-size selection. A comparison between Jacobi and Democratic Heliocentric coordinates shows that the former performs best when orbits are nested, while the latter is better suited to systems with crossing or unordered orbits. These findings provide practical guidelines for applying Wisdom–Holman integration effectively across a range of dynamical regimes.

The Shallow Water Equations (SWEs) for ocean applications can be discretized using finite differences, resulting in a system of time-dependent ordinary differential equations (ODEs). These ODEs can then be solved on a GPU using various time-integration schemes, which can be categorized as explicit and implicit methods. The primary aim of this thesis is to evaluate the performance of various time-integration solvers implemented on a GPU for a simplified tidal model of the North Sea. The investigation includes a comparison of explicit second-, third-, and fourth-order Runge-Kutta (RK) and multistep methods as well as several second-order implicit schemes. Moreover, a novel approach is proposed for solving the tidal model and addressing the nonlinear systems within the implicit time iterations. This approach is a combination of an implicit SDIRK2-scheme with a pseudo-time-stepping approach and a multi-level technique. All numerical schemes are implemented on the GPU using the Julia programming language. The most efficient explicit time-integration scheme was RK4. However, on a high resolution grid , the newly developed implicit solver outperformed RK4, in terms of speed.

Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures, which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn wounds is crucial for developing effective treatment strategies. Traditional mathematical models, while accurate, are often computationally expensive and time-consuming, limiting their practical application. Recent advancements in machine learning, particularly in deep learning, offer promising alternatives for accelerating these predictions. This study investigates the use of a deep operator network (DeepONet), a type of neural operator, as a surrogate model for finite element simulations for predicting post-burn wound evolution. We trained DeepONets on various wound shapes, enhancing the architecture by incorporating initial wound shape information and applying sine augmentation to enforce boundary conditions. The most sophisticated model achieved an R² score of 0.9960, indicating strong predictive accuracy. Additionally, the model generalised well to convex combinations of basic shapes, with an R² score of 0.9944, and provided reliable predictions over an extended period of up to one year. These findings suggest that DeepONets can effectively serve as a surrogate for traditional finite element methods in simulating post-burn wound evolution, with potential applications in medical treatment planning.

This study introduces KarGus, a novel system for multi-document question answering (MD-QA) designed for diverse domains. KarGus integrates advanced Natural Language Processing techniques with Knowledge Graph (KG) construction and Graph Neural Networks (GNNs) to enhance retrieval performance across various specialized fields.
We explore the efficacy of combining semantic similarity, TF-IDF, and Named Entity Recognition features in KG construction and information retrieval. Experimental evaluation on a corpus of 30 documents (1810 pages, 10,853 text chunks) from corporate intelligence demonstrates that KarGus outperforms traditional embedding-based methods, achieving a Recall@5 of 0.850 compared to the baseline's 0.823 (p < 0.05). The optimal configuration emphasized semantic similarity (weight 0.75), keyword relevance (0.2), and entity information (0.05).
Analysis of the KG structure revealed moderately well-defined community structures and efficient information traversal properties. While GNN models showed promising training results, they underperformed in the retrieval task, highlighting challenges in GNN application to MD-QA.
This research contributes to the field of information retrieval by demonstrating the efficacy of integrating NLP techniques with graph-based approaches in MD-QA. The adaptable nature of KarGus suggests potential applications across various specialized domains. Future work will focus on validating cross-domain performance and refining GNN implementations for diverse retrieval tasks.

The goal of the thesis is to find a Reduced Order Modelling method that speeds up burnup simulations—as encountered in the core of a Molten Salt Fast Reactor—while keeping
accuracy loss minimal. Four different methods have been tested: Proper Orthogonal Decomposition (POD), heuristically corrected POD, Balanced Truncation (BT), and Balanced
Proper Orthogonal Decomposition (BPOD). The first two methods are inadequate, because
of stability issues. The third is stable, but fails to execute for burnup simulations. The
fourth, a midway method between the first and third, does work for burnup simulations.
Using BPOD with 4 orders for a 10 year burnup simulation of 1650 nuclides with 1000
simulation steps, we find a normalised relative error of 10^-5 both for the total model and
each nuclide individually. The execution time per simulation step is reduced to 10^-5 s.
These results are a factor 1000 better than known alternatives such as the ORIGEN burnup
program.

The conclusion contains recommendations for incorporating different fuel mixtures and non-
linearity of the burnup equation in the BPOD. The method could be generalised to handle
arbitrary burnup problems with a single Reduced Order Model.

To optimally use wind farms, thorough understanding of wind patterns is needed. Recently, a lot of attention in the scientific community is turned to the Current FeedBack effect, where oceanic currents influence the atmosphere above. It has been shown that this also applies to tidal currents in the English Channel where the induced tidal winds have an amplitude of one-third of the underlying current. In this report focus is moved to the Dutch coast. Using a numerical integration model of a vertical grid, the horizontal wind speeds above a small area of the Dutch coast are modelled. The model is based on the 1-dimensional Navier-Stokes equations in combination with Prandtl's mixing length model to account for turbulence. The horizontal wind speeds are found to reach up to one-fourth of the amplitude of the tidal currents at a height of z = 10 m above the sea surface and 1/20 at z = 50 m. This is similar to what was found in earlier research, but a lot of assumptions were made in this model. Therefore, further research could focus on addressing some of these assumptions such that the understanding of tidal induced wind velocities can be even better understood.

This thesis focuses on the influence of tides on flow behaviour and salt intrusion in a semi-infinite channel ending at the sea, with a specific focus on the effects of adding a side channel. Tide causes variations in the flow behaviour, which in turn affects salt concentrations in the channel. Adding a side channel has an impact on the flow pattern, mainly because of reflections of the tidal wave, leading to changes in the salt intrusion. The effect investigated is the influence of varying the distance from the sea to the junction, and the length of the side channel. A 1-dimensional exploratory model based on the shallow water equations for the flow behaviour is developed, analysing only the bidaily M2 tide caused by the gravitational pull of the moon. The flow pattern is solved analytically, while the salt balance is solved analytically in time but numerically in space. The salt balance contains an advection term and an effective dispersion term. The effect of adding a branching channel is compared to the same situation without a branching channel. It is found that the addition of a side channel affects the salt intrusion in the order of 1 km compared to a single channel. Moreover, both positive and negative changes occur in the shift of the intrusion length. The results of this study can be used to understand and explain the behaviour in more complex geometries.

The computational demands of finite element simulations, particularly in predicting the time-dependent response of high-dimensional non-linear dynamical systems, pose significant challenges. To overcome these challenges, researchers have developed model order reduction (MOR) methods, which aim to reduce computational complexity by utilizing lower-dimensional models. This thesis proposes a MOR technique that simultaneously learns both the projection to, and the reduced dynamics on, a lower-dimensional manifold using autoencoders, a type of neural network. During training, the known linear part of the reduced dynamics is used to aid the optimization process, leading to an effective method of simultaneous projection and linear informed training (SPLIT). SPLIT demonstrates outstanding performance on the test case of a 2D cantilever beam, and is capable of making non-linear forced response predictions, even though being trained on unforced decaying trajectories. Even in scenarios involving highly non-linear behaviour, such as when the beam folds over itself, SPLIT continues to make accurate predictions, while other MOR techniques fail. This work highlights the potential of autoencoders to advance the field of MOR and improve the efficiency and reliability of simulations for complex dynamical systems.

The whitening transformation transforms a random matrix into a whitened matrix with expectation 0 and covariance matrix I. By removing the first and second order statistical structures, higher order structures can be looked at for better classification. This is why Stage Gate 11 B.V. has employed whitening in the preprocessing of their hyperspectral data. The aim of this work is to gain insight into the whitening transformation and how it influences hyperspectral data.
To gain this insight, synthetic data was created and used to make synthetic scans. The signal-to-noise ratio of a target spectrum was calculated, and Monte Carlo simulations were used to reveal hidden patterns in the data. In case of a high contrast scenario, multi-area whitening was employed and the cosine similarity between the target spectrum and its signature was determined. It was observed that the shape and intensity of the whitened target spectrum differs, depending on if pixels were used as observations or wavelengths. However, both are subject to the ‘bleeding’ effect. Further, it was found that if the number of pixels in the scan is greater than the number of spectral bands (548), then the signal-to-noise ratio becomes better as the number of whitened pixels in the scan increases. In case of a high contrast scenario, multi-area whitening guarantees the uniformity of the spectra, resulting in a higher
cosine similarity between the target spectrum and its signature. But as multi-area whitening uses a smaller
number of pixels in the scan, it cannot be concluded if multi-area whitening is better than global whitening, as it is not known how the increase in cosine similarity and the decrease in signal-to-noise ratio relate to the classification process. Finally, it is concluded that when working with real and unknown data, using pixels as
observations is much more feasible.

During the initial phase of diagnosis, patients with anti-NDMA-receptor encephalitis (anti-NMDARE) often experience severe symptoms that significantly impact their quality of life. Anti-NDMARE is an autoimmune disorder affecting the brain, with electroencephalography (EEG) playing a vital role in diagnosis and treatment. Identifying EEG patterns associated with positive or negative prognosis is crucial for adjusting treatment intensity. Improved understanding of diagnosis, prognosis and treatment could enhance the quality of life for anti-NDMARE patients. This thesis aimed to analyse the EEG data with Machine Learning (ML) to predict which patients exhibit positive recovery after 12 months of standard treatment.

To predict the outcome after 12 months, a Random Forest (RF) classifier was constructed using available EEG features. The EEG dataset exhibited a clustered structure due to multiple values for each patient’s EEG features. Three approaches were considered to handle this clustering: ignoring clustering, reducing clustering to independent observations, and explicitly accounting for clustering. The first two options were explored in this research. Another prominent challenge encountered early in the research was the class imbalance, which was addressed by under- and oversampling the dataset.

For the simulation sets, under- or oversampling did not yield the desired effect, as the normal sets demonstrated comparable or even superior performance compared to the the under- and oversampled sets. However, under- and oversampling improved the performance scores for the real dataset. Reducing the clusters to independent observations did not achieve high performance scores compared to ignoring clustering, both in the simulation and real data cases. Furthermore, in both cases, RF models using the EEG sets outperformed those using principal component analysis (PCA) on the clustered EEG set.

Although the performance metrics scores were not yet optimal, important features for determining class labels were identified, providing a good understanding of the dataset. Mean Decrease in Impurity (MDI) and SHAP algorithm highlighted the significance of connectivity-related features in the reduced clustering to independent observation setting. The relevance of these features became evident upon calculating the mean, minimum, or maximum. In the EEG setting, MDI emphasized the importance of the features deltapower, sampleentropy and occipital-related features. These features remain important in the reduced set. SHAP, in addition to prioritizing the same features, offered insights into how specific features contribute to the prediction of a specific observation, enhancing interpretability.

The challenges for the RF classifier in the case of anti-NDMARE are class imbalance and accurate classification of the minority class. Under- and oversampling techniques successfully improved classification of minority class observations for the original EEG set. Concluding, this set is strongly encouraged to be utilized over all sets when aiming to classify EEG features. However, this set overlooks the clustering aspect, leaving room for optimization in future research to address this limitation. Additionally, it is recommended to explore the potential of a Convolutional Neural Network (CNN) for accurate classification of raw EEG signals. Its exploration was beyond the scope of this research.

Tidal flats are important coastal ecosystems that support a diverse range of plants and animals. Accurate prediction of water motion over tidal flats is crucial for the design of coastal infrastructure, hazard assessment, environmental management and oceanography research. Defina [1] derived a new set of shallow water equations that allow for water motion prediction in partially dry domains. Existing methods for predicting water motion are limited by numerical stability and accuracy, and require high-quality input data. Using the periodic behaviour of tides, this thesis introduces a new method in the frequency domain. The method is tested and compared to a fully numerical solution. The results of the linearised classical shallow water equations encourage future research required for the statistical shallow water equations that allow partially dry domains.

This research investigates the impact of gravitational scatterings caused by close encounters between particles in an N-body Kepler system, addressing three main questions: (1) the influence of scatterings on system evolution, (2) the correspondence between simulated and expected average times between scatterings, and (3) the effect of increasing different parameters individually on the average scattering time. Simulations demonstrate an average scattering angle of 15.2 degrees for particles involved in the top 10 percent of scatterings. This would indicate a non-negligible impact of gravitational scatterings, especially for systems with heavier bodies. The results indicate that the simulated average time between scatterings is higher than the expected average, necessitating further research for accurate estimation. Moreover, the time between scatterings decreases over time, before reaching a stationary state after roughly 300 scatterings. On this domain, the correlation coefficient between the scattering time and the scattering counter was found to be  -0.08. By varying the test domains for different parameters, a new expression for the expected time between two scatterings is proposed based on simulation data. A clear connection was found between the scattering time and the number of particles, the maximum orbital radius and the maximum inclination angle. The study acknowledges limitations, including the non-stationary initialization state and linear approximations to most computations, suggesting avenues for future improvement. Overall, this research aims to find the role of gravitational scatterings in Kepler systems and underscores the need to consider these interactions, which are now often considered to be negligible.

Ocean currents play a crucial role in many scientific and industrial applications. Contemporary measurement techniques are limited in spatial coverage or spatial resolution. This study presents a proof-of-concept for a new measurement principle that merges optical satellite imagery of Kelvin wakes with data from the Automatic Identification System (AIS). A case study in the Strait of Gibraltar was performed using two months of Sentinel-2 imagery, which yielded 81 visible Kelvin wakes over 25 images. For each Kelvin wake, currents were estimated in directions parallel and perpendicular to the ship's sailing line. The estimated currents were validated with respect to surface currents derived from High-Frequency Radars (HFRs) and modelled currents from the Copernicus Marine Environmental Monitoring Service (CMEMS). The results suggest that the estimated currents were highly accurate in the absence of large variations in ship course. However, the frequency of measurements is limited by satellite repeat times and Kelvin wake visibility. More research is needed to explore the potential spatiotemporal distribution of measurements.

Computational power is a challenge when it comes to the high-fidelity modeling of nuclear reactors. Detailed simulations of reactor physics involve complex calculations that require significant computing resources, which can be time-consuming and expensive. Reduced Order Modeling (ROM) allows for an approximation of a complex model by only capturing the essential features, thereby reducing the computational load. A reduced order model provides computationally efficient approximations of a system, but it requires still many evaluations of a high-fidelity model to capture all the dynamics. Using the adaptive sparse grid can reduce the number of evaluations needed, though the construction of the reduced order model is still computationally intensive.

The aim is to minimize the computational workload involved in constructing a reduced-order model during the offline phase. This is achieved by decreasing the number of high-fidelity model evaluations necessary for building the reduced order model while maintaining accurate results. To this end, the existing adaptive proper orthogonal decomposition algorithm is enhanced by employing multi-fidelity techniques. Multi-fidelity methods aim to combine large amount of low-fidelity data with a limited amount of high-fidelity data to compute accurate, yet computationally inexpensive approximations. Two novel multi-fidelity reduced order model methods based on proper orthogonal decomposition are proposed; Filtered Bi-Fidelity Adaptive Proper Orthogonal Decomposition (FB-POD) algorithm and Adapted Bi-Fidelity Proper Orthogonal Decomposition (AB-POD). These models are evaluated on two different test cases, and the balance between the accuracy of each multi-fidelity ROM and the computational cost, measured by the number of high-fidelity evaluations, is investigated. In specific cases, the proposed methods significantly reduce the number of high-fidelity evaluations compared to the single high-fidelity ROM, while yielding comparable accuracy.

In the realm of fluid dynamics and particle transport, the control of particle trajectories represents a formidable challenge. It would be useful to be able to optimally navigate an oceanographic float from one pre-set location to another by solely changing its buoyancy. In this thesis, a first step in discovering whether this is possible and what optimization strategy can be used is taken.
To do so, first, the physical situation is translated into a mathematical model. Then, an optimization strategy for changing the buoyancy to optimally travel to a set location is constructed. The strategy is based on gradient descent and implemented in Python. Four different definitions of an optimal trajectory to a target location are considered, those are 1) any trajectory that leads to the target location, 2) the most time-efficient trajectory, 3) the most energy-efficient trajectory, and 4) a trajectory that is both time and energy-efficient.
The optimization strategy is tested for five different starting and target locations for a small spherical float in an idealized two-dimensional linear flow field. It is concluded that it is possible to use the optimization strategy to navigate a float using buoyancy changes for all four optimization objectives, although the current implementation is not efficient enough for targets far away.
The first objective of future research should be to increase the coding efficiency. Thereafter, other steps toward a more realistic situation can be taken, such as testing for non-linear flow fields, three-dimensional fields, and bigger floats.

Even though the use case of this study was to predict water currents for the sailing regatta in Tokyo, the method can be used for many different applications.

Cardiac complications after surgery are common irrespective of the underlying condition. The postoperative level of troponin T is a good marker for cardiac complications. Little is known on the pathology of the release of troponin T in the blood, while a better understanding might provide the ability to reduce the complications. The goal of the thesis is to find patterns in intraoperative data that are related to the release of troponin T in the blood during surgery. The states resulting from estimating an MSVAR on intraoperative hemodynamic data were interpreted and related to postoperative troponin T measurements. The MSVAR was estimated in two ways: with the EM algorithm and in Bayesian fashion with the Gibbs sampler. Prior distributions were chosen and a Gibbs sampler was developed for estimating the MSVAR with these priors. The differences between the EM algorithm and the Gibbs sampler are mostly fundamental and not practical. Furthermore, the MSVAR is an appropriate model for modelling intraoperative hemodynamic data. The states of the MSVAR were related to various surgery variables, but did not have any prognostic value for predicting postoperative troponin T. The states related to the external shocks continuously given to the patient during surgery rather than the patient's state.