Searched for: subject%3A%22Differential%255C%252BEquations%22
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Bakker, Bo (author)
Data-driven approaches are a promising new addition to the list of available strategies for solving Partial Differential Equations (PDEs). One such approach, the Principal Component Analysis-based Neural Network PDE solver, can be used to learn a mapping between two function spaces, corresponding to a PDE. However, the practical limitations of...
bachelor thesis 2024
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Kiste, Amund (author)
Solving Partial Differential Equations (PDEs) in engineering such as Navier-Stokes is incredibly computationally expensive and complex. Without analytical solutions, numerical solutions can take ages to simulate at great expense. In order to reduce this cost, neural networks may be used to compute approximations of the solution for use during...
bachelor thesis 2024
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Lacombe, Pablo (author)
This paper presents a comprehensive exploration of a novel method combining Principal Component Analysis (PCA) and Neural Networks (NN) to efficiently solve Partial Differential Equations (PDEs), a fundamental challenge in modeling a wide range of real-world phenomena. Our research extends the work of Bhattacharya et al. by focusing on PCA for...
bachelor thesis 2024
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Verton, Max (author)
We analyze the spatially discretized version of the Allen-Cahn partial differential equation. The second order derivative is numerically approximated by a weighted infinite sum. The coefficients of this sum as well as the function f in the differential equation have got freedom inside determined restrictions. For this spatially discretized...
bachelor thesis 2023
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Halevy, Avi (author)
In this work residual error estimates are constructed using Neural Networks for Finite Element Method. These can be used to do adaptive mesh refinement. Two neural networks are developed the Multilayer Perceptron and the Transformer model. The error estimates are made for 1d poisson equations but the idea will generalise to higher dimensions as...
bachelor thesis 2022
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Daemen, Mieke (author)
The main aim of the research presented in this report is investigating analytical methods to model fluid-structure interaction in large-scale offshore floating photovoltaics. The model that was attempted to be solved analytically is based on a model presented by Pengpeng Xu (2022).<br/>The dimensions in the equations were removed. Applying a...
bachelor thesis 2022
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Zegers, Samuel (author)
In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’,...
bachelor thesis 2022
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van Ooijen, Cas (author)
This thesis is about the wave equation. The wave equation describes waves that propagate through a certain medium. The solution of the wave equation is a mathematical description of what that wave looks like. There are many fields of study where the wave equation is used to model processes that behave like travelling waves. For instance, a...
bachelor thesis 2022
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Hendriks, Leo (author)
This essay shows a two dimensional implementation of the finite element method for the Westervelt equation. To do this the finite element method is first applied to the linear wave equation, then to non-linear diffusion and finally to the Westervelt equation. Both an element by element and a faster vectorized implementation are given for the...
bachelor thesis 2021
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Vural, Asya (author)
The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a non-linear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.<br/>This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through...
bachelor thesis 2021
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de Jong, Sam (author)
The Ekman spiral is described by a coupled system of differential equations originally discussed by Walfrid Ekman (Ekman, 1905). This system is a simplified version of the Navier­Stokes equations. The differential equations, as discussed in Ekman’s paper, concern the currents of the ocean. However, it is also possible to interpret these...
bachelor thesis 2021
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Brouwers, David (author)
In this bachelor thesis we use a stochastic model to aspire to explain biodiversity patterns in different ecosystems with selection advantage. The stochastic model we use is an extension of the mean­-field voter model where we include a selection factor. In the model individuals with two different types of alleles in two different ecosystems are...
bachelor thesis 2021
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Leeuwis, Toby (author)
When transforming PDE problems using Fourier and Laplace transforms, we can find functions that represent the problem, and which can be used to determine properties of the problem. We define such functions as symbols $P(\lambda,z)$. In general, we define the class of symbols $S(L_t\times L_x)$ are all functions which are represented by a...
bachelor thesis 2021
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Frima, Erik (author)
In (mathematical) physics one can encounter problems with a fase change, the so called Stefan problems. Numerical methods to solve these problems often use a level-set function which indicates the distance to the fase boundary. Problems can arise in the medial axis points of the zero set. Therefore it can be usefull to calculate this medial axis...
bachelor thesis 2021
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van Vliet, Christiaan (author)
In this work neural networks are used to approximate the solutions of multiple differential equa- tions. Three main differential equations are investigated: the mass-spring equation, the heat equation and the Navier-Stokes equations coupled with the continuity equation. Each of these equations are approached differently with the current methods,...
bachelor thesis 2021
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Vos, Bart (author)
In recent years many automatic differentiable programming frameworks have been developed in which numerical programs can be differentiated through automatic differentiation (AD). Examples of these frameworks are Theano, TensorFlow and Pytorch. These frameworks are widely used in Machine Learning. AD also finds applications in the field of...
bachelor thesis 2021
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Goudsmit, L. (author)
In the ocean resides a large amount of plastic. This has severe environmental consequences for the oceans. To be able to clean up all this plastic the location of the plastic is needed. A lot of times plastic is cleaned up at the source, but to clean up here this location needs to be known. However, what if the start location is not known and...
bachelor thesis 2020
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Blok, S.A.W. (author)
In financial and egineering problems, we are often faced with solving Partial-Integro Differential Equations (PIDEs). Rarely we can find an analytic solution in a closed form expression for these PIDEs, hence we turn to numerical schemes to accurately approximate the solution instead. Classically these methods are based on finite difference...
bachelor thesis 2020
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Wisse, A.C. (author)
This thesis considers the thin-film equation in partial wetting. The mobility in this equation is given by h<sup>3</sup>+λ<sup>3-n</sup>h<sup>n</sup>, where h is the film height, λ is the slip length and n is the mobility exponent. The partial wetting regime implies the boundary condition dh/dz&gt;0 at the triple junction....
bachelor thesis 2020
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Ha, Deon (author)
With the growing wealth and economy of a country, there are an increasing amount of small and big businesses. Every company has its own marketing strategy that it uses in order to lure customers away from their competition and increase their sales. Choosing the perfect time to advertise or discount several products is of essence for a company to...
bachelor thesis 2019
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