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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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Négyesi, B. (author), Andersson, Kristoffer (author), Oosterlee, Cornelis W. (author)A novel discretization is presented for decoupled forward–backward stochastic differential equations (FBSDE) with differentiable coefficients, simultaneously solving the BSDE and its Malliavin sensitivity problem. The control process is estimated by the corresponding linear BSDE driving the trajectories of the Malliavin derivatives of the...journal article 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 non-linear fractional differential equations, subject to integral boundary conditions. We use a parametrization technique and a dichotomy-type approach to reduce the original problem to two “model-type” fractional boundary value problems with linear two-point boundary conditions. A numerical-analytic technique is applied...journal article 2024
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Binatari, N. (author), van Horssen, W.T. (author), Verstraten, P. (author), Adi-Kusumo, F. (author), Aryati, L. (author)In this paper, we present a new approach on how the multiple time-scales perturbation method can be applied to differential-delay equations such that approximations of the solutions can be obtained which are accurate on long time-scales. It will be shown how approximations can be constructed which branch off from solutions of differential...journal article 2024
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Blom, H.A.P. (author)The transition kernel of an ℝ <sup>n</sup>-valued diffusion or jump diffusion process {X <sub>t</sub>} is known to satisfy the Feller property if {X <sub>t</sub>} is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X <sub>t</sub>} is the solution of an SDE whose coefficients...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 semi-linear 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 inverter-based resources in the power grid, it is pertinent for present-day 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 solar-sail near-Earth 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 energy-conservative data-driven approach in modelling the closure terms of the Navier-Stokes 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 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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Böhm, Udo (author)The stochastic FitzHugh-Nagumo 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 well-posedness and regularisation results for the FitzHugh-Nagumo 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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Agresti, A. (author), Veraar, M.C. (author)In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up 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 non-smooth...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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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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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 high-fidelity 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 space-time...master thesis 2022