Browsing NTNU Open by Author "Owren, Brynjulf"
Now showing items 1-20 of 44
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A Library for Computing with Trees and B-Series
Sundklakk, Henrik Sperre (Master thesis, 2015)Unordered rooted trees and B-series can be used to analyze the properties of many one-step methods for autonomous ordinary differential equations. This thesis describes aspects of trees and B-series necessary to use them ... -
Adaptive energy preserving methods for partial differential equations
Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article; Peer reviewed, 2017)A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of ... -
Applications of splitting Methods and exponential Integrators to an electro-chemical Heart Cell Model
Gjerald, Sjur (Master thesis, 2007)In this thesis we discuss how a system of ordinary differential equations (ODE) describing electro-chemical processes in a heart cell can be solved by numerical methods. The system is stiff, and explicit numerical solvers ... -
Combining Artificial Neural Networks with Reduced Order Models with Applications to Classification Problems
Breivik, Liv (Master thesis, 2023)Denne avhandlingen er en konseptutføring for reduksjonsteknikker for nevrale nettverk. Modellen som er blitt redusert er VGG-16-modellen, som er trent på augmenterte versjoner av både CIFAR-10-datasettet og SVHN-datasettet. ... -
Community Detection in Large Social Networks
Olsen, Mats Julian (Master thesis, 2014)I denne masteroppgaven implementeres og testes to algoritmer for å finne gruppe- struktur i nettverk, nemlig Louvain-metoden og Diffusion and Propagation-metoden. Et nettverks gruppestruktur består av en naturlig inndeling ... -
Computational geometric methods for preferential clustering of particle suspensions
Tapley, Benjamin Kwanen; Andersson, Helge Ingolf; Celledoni, Elena; Owren, Brynjulf (Peer reviewed; Journal article, 2022)A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the ... -
Coordinate maps for Lie group integrators applied to mechanical systems
Mathiassen, Maja Bjørge (Master thesis, 2022)Liegruppeintegratorer er numeriske metoder brukt til å løse differensiallikninger som utvikler seg på mangfoldigheter via Liegruppevirkninger. I denne masteroppgaven introduseres en type Liegruppeintegrator som kalles ... -
Deep learning as optimal control problems: models and numerical methods
Benning, Martin; Celledoni, Elena; Ehrhardt, Matthias J.; Owren, Brynjulf; Schönlieb, Carola-Bibiane (Journal article; Peer reviewed, 2019)We consider recent work of [11] and [6], where deep learning neuralnetworks have been interpreted as discretisations of an optimal control problemsubject to an ordinary differential equation constraint. We review the first ... -
DETECTING AND DETERMINING PRESERVED MEASURES AND INTEGRALS OF BIRATIONAL MAPS
Celledoni, Elena; Evripidou, Charalambos; McLaren, David I.; Owren, Brynjulf; Quispel, G.R.W.; Tapley, Benjamin Kwanen (Peer reviewed; Journal article, 2022)In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use ... -
Discrete gradient methods in image processing and partial differential equations on moving meshes
Ringholm, Torbjørn (Doctoral theses at NTNU;2018:235, Doctoral thesis, 2018) -
Discrete Invariant Variational Problems
Bogfjellmo, Geir (Master thesis, 2011)This thesis studies variational problems invariant under a Lie group transformation, and invariant discretizations of these. In chapters two and three, a general method for creating symplectic integrators preserving certain ... -
Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article; Peer reviewed, 2018)This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This ... -
Energy preserving methods on Riemannian manifolds
Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article, 2018)The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. ... -
Energy-preserving numerical methods for differential equations: Linearly implicit methods and Krylov subspace methods
Li, Lu (Doctoral theses at NTNU;2019:272, Doctoral thesis, 2019) -
Equivariant neural networks for inverse problems
Celledoni, Elena; Ehrhardt, Matthias J.; Etmann, Christian; Owren, Brynjulf; Schönlieb, Carola-Bibiane; Sherry, Ferdia (Peer reviewed; Journal article, 2021)In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of ... -
Geometric and integrability properties of Kahan?s method: The preservation of certain quadratic integrals
Celledoni, Elena; McLaren, David; Owren, Brynjulf; Quispel, Reinout (Peer reviewed; Journal article, 2019)Given a quadratic vector field on possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discretization method exactly preserves a nearby modified ... -
Geometric integration of nonlinear wave equations
Dahlby, Morten Lien (Master thesis, 2007)We give an short introduction to the Camassa-Holm equation and its travelling wave solutions. Many well-known equations in mathematical physics describe geodesic flows on appropriate Lie groups. The choice of group and ... -
Group Equivariant Convolutional Neural Networks
Rød, Marcel Heshmati (Bachelor thesis, 2020)Å oppdage og klassifisere gjenstander i et bilde er en viktig underoppgave i bygge algoritmer som samhandler med den virkelige verden. I moderne applikasjoner, blir denne oppgaven løst ved hjelp av dyp læring med konvolverede. ... -
An integral model based on slender body theory, with applications to curved rigid fibers
Andersson, Helge Ingolf; Celledoni, Elena; Ohm, Laurel; Owren, Brynjulf; Tapley, Benjamin (Peer reviewed; Journal article, 2021)We propose a novel integral model describing the motion of both flexible and rigid slender fibers in viscous flow and develop a numerical method for simulating dynamics of curved rigid fibers. The model is derived from ... -
Integral Preserving Numerical Methods on Moving Grids
Eidnes, Sølve (Master thesis, 2013)Integral preservation for ordinary and partial differential equations is defined, and the integral preserving discrete gradient methods and discrete variational derivative methods on fixed grids are given, with a formal ...