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Bakker, Bo (author)Datadriven approaches are a promising new addition to the list of available strategies for solving Partial Differential Equations (PDEs). One such approach, the Principal Component Analysisbased 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 NavierStokes 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 realworld phenomena. Our research extends the work of Bhattacharya et al. by focusing on PCA for...bachelor thesis 2024
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Successive approximations and interval halving for fractional BVPs with integral boundary conditionsMarynets, K. (author), Pantova, D.H. (author)We study a system of nonlinear fractional differential equations, subject to integral boundary conditions. We use a parametrization technique and a dichotomytype approach to reduce the original problem to two “modeltype” fractional boundary value problems with linear twopoint boundary conditions. A numericalanalytic technique is applied...journal article 2024
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Agresti, A. (author), Veraar, M.C. (author)In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi or semilinear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz...journal article 2024
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Krishnakumar, Nila (author)To keep pace with increasing renewable energy penetration and consequent increase in inverterbased resources in the power grid, it is pertinent for presentday research to address the resulting drop in system inertia levels and its impact on frequency stability. With decreasing levels of inherent rotational inertia present in the system, any...master thesis 2023
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Garcia Bonilla, Juan (author)Solar sailing is a promising propellantless propulsion method that employs large reflective surfaces to harness solar radiation pressure for spacecraft propulsion. Despite the fact that several solarsail nearEarth missions will launch in the coming years, there is notable lack of published studies on the uncertainties associated with missions...master thesis 2023
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Bettini, Andrea (author)This thesis presents an energyconservative datadriven approach in modelling the closure terms of the NavierStokes equations casted through the Variational Multiscale (VMS) framework. For context, the VMS framework is applied in designing stabilised finite element methods for multiscale phenomena in which stability is not guaranteed. Under...master thesis 2023
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Verton, Max (author)We analyze the spatially discretized version of the AllenCahn 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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Böhm, Udo (author)The stochastic FitzHughNagumo equations are a system of stochastic partial differential equations that describes the propagation of action potentials along nerve axons. In the present work we obtain wellposedness and regularisation results for the FitzHughNagumo equations with domain R^d. We begin by considering the weak critical variational...master thesis 2023
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Vuik, Cornelis (author), Vermolen, F.J. (author), van Gijzen, M.B. (author), Vuik, Thea (author)In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We conﬁne ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation....book 2023
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Takali, Farid (author), Nirwal, Sonal (author), Othmani, Cherif (author), Groves, R.M. (author)It has been shown that the roots of guided waves in laminate plates produced by the ordinary differential equations (ODE) approach may not hold under to some computational conditions. A particular drawback of the 2D formulation of the ODE approach is the lack of reliability in the case of unidirectional laminates due to the decoupling...journal article 2023
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Agresti, A. (author), Veraar, M.C. (author)In this paper we consider a class of stochastic reactiondiffusion equations. We provide local wellposedness, regularity, blowup criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of nonsmooth...journal article 2023
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van Kan, J.J.I.M. (author), Segal, A. (author), Vermolen, Fred (author)Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the...book 2023
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Thorpe, Matthew (author), van Gennip, Y. (author)Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The contribution of this paper is to show that, for the residual neural network model, the deep layer limit...journal article 2023
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Hadjisotiriou, George (author)Compositional simulation is computationally intensive for highfidelity models due to thermodynamic equilibrium relations and the coupling of flow, transport and mass transfer. In this report, two methods for accelerated compositional simulation are outlined and demonstrated for a gas vaporization problem. The first method uses a proxy model...master thesis 2022
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Titulaer, Björn (author)Spatiotemporal stochastic processes have applications in various fields, but they can be difficult to numerically approximate in a reasonable time, in particular, in the context of statistical inference for large datasets. <br/>Recently, a new approach for efficient spatiotemporal statistical modeling has been proposed, where the spacetime...master thesis 2022
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Ul Haq, Rana (author)Convectiondominated flow problems are wellknown to have nonphysical oscillations near steep gradients or discontinuities in the solution when solved with standard numerical methods, such as finite elements or finite difference methods. To overcome this limitation, algebraic flux correction (AFC) can be used, which is a stabilization method....master thesis 2022
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Lok, Pieter (author)The performance of hydrostatic bearings is in part decided by their lubricationfilm height shape. Imaging the shape can be done by dissolving fluorescent dyes in the layer. However, current imaging techniques are rooted in heuristics, and as such, their physics, design parameters, and error sources are not quantitively understood. To fully...master thesis 2022
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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