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van Rhijn, J. (author)Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. This thesis investigates if GANs can be used to provide a strong approximation to the solution of stochastic differential equations (SDEs) of the Ito type. Standard GANs are only able to...master thesis 2020
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Négyesi, Bálint (author)Backward stochastic differential equations (BSDE) are known to be a powerful tool in mathematical modeling due to their inherent connection with secondorder parabolic partial differential equations (PDE) established by the nonlinear FeynmanKac relations. The fundamental power of BSDEs lies in the fact that with them one does not merely obtain...master thesis 2020
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de Boer, S.G. (author)This thesis showcases a rather contemporary method of solving a generalized system of stochastic differential equations (SDE's) comparable to the SABR model. The solution is derived from a stochasticlocal volatility (SLV) model in which the local volatility (LV) component is kept general. This generality is maintained throughout all derivations...master thesis 2020
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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 PartialIntegro 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 thinfilm equation in partial wetting. The mobility in this equation is given by h<sup>3</sup>+λ<sup>3n</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>0 at the triple junction....bachelor thesis 2020
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Marynets, K. (author)We deal with a system of quasilinear fractional differential equations, subjected to the Cauchy–Nicoletti type boundary conditions. The task of explicit solution of such problems is difficult and not always solvable. Thus we suggest a suitable numerical–analytic technique that allows to construct an approximate solution of the studied...journal article 2020
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Prasse, B. (author), Van Mieghem, P.F.A. (author)The majority of epidemic models are described by nonlinear differential equations which do not have a closedform solution. Due to the absence of a closedform solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the Nintertwined meanfield approximation of the susceptible...journal article 2020
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Jongbloed, Henk (author)Reliable and efficient modelling of magnetic hysteresis in inhomogeneous and anisotropic media is an important step in developing a stateoftheart closedloop 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...master thesis 2019
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Shachor, Benny (author)Understanding the permeability of the subsurface is a crucial step to simulate fluid flow in the subsurface. A parameter estimation problem for the flow equations can be solved to find the permeability. The robust identification of material parameters remains a significant challenge. In classical approaches, the nonlinear leastsquares problem...master thesis 2019
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Keetch, Blaine (author), van Gennip, Y. (author)The MaxCut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the vertex set of G into two disjoint subsets. For an unweighted graph, the size of the cut is the number...journal article 2019
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Corstanje, Marc (author)When data in higher dimensions with a certain constraint on it, say a set of locations on a sphere, is encountered, some classical statistical analysis methods fail, as the data no longer assumes its values in a linear space. In this thesis we consider such datasets and aim to do likelihoodbased inference on the center of the data. To model the...master thesis 2019
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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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van de Kamp, Carsten T. (author)We consider adaptive network models with discrete and continuous state sets obeying dynamical rules that enable application to swarming systems. The 2state adaptive network contains a supercritical pitchfork bifurcation in the transition between ordered and disordered stationary solutions. We derive an adaptive network model that works on a...bachelor thesis 2019
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Hermans, Carlos (author)This thesis investigates several kinds of models of describing multicommodity dynamical flow. Three models have been developed for a spatial logistic network, on which packages are delivered by vehicles and another<br/>model was developed to describe interactions between the customers, the stores and the deliverers, which does not explicitly...master thesis 2019
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Li, Vincent (author)In this thesis the stability type of y=0 is being considered for the delay differential equation y''(t) + ay(t) + by(t1) = 0 with a and b real numbers. It is already known that y=0 is stable when b=0 and a>0 and unstable when b=0 and a<0. The aim of this project is to determine the stability of y=0 for all values of a and b. First, the...bachelor thesis 2019
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van der Meer, Remco (author)Recent works have shown that neural networks can be employed to solve partial differential equations, bringing rise to the framework of physics informed neural networks.The aim of this project is to gain a deeper understanding of these novel methods, and to use these insights to further improve them. We show that solving a partial differential...master thesis 2019
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Verbist, Victor (author)A model is developed to simulate NaCl concentrations across a cation exchange membrane in the transient regime. The convectionless NersntPlanck equation is combined with the continuity equation to obtain a partial dierential equation in time and space. The boundary conditions at the edges of the cell for this equationare a constant bulk...bachelor thesis 2019
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den Hertog, Wilbert (author)The numerical errors involving the application of the levelset method to a problem can be minimized by fitting a mesh (usually a triangular mesh in two dimensions) to the zero levelset curve defined by the levelset function. These numerical errors depend on two things: the size and skewness of the triangles in the mesh. To fit the mesh, Timo...bachelor thesis 2019
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Oude Luttikhuis, Jurjen (author)It is possible to estimate derivatives of real functions with complex methods. These complex methods can increase speed or accuracy. The functions needs to be known to determine the derivative with a complex method.bachelor thesis 2019