Now showing items 21-40 of 50

    • 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 ...
    • Krylov projection methods for linear Hamiltonian systems 

      Li, Lu; Celledoni, Elena (Journal article; Peer reviewed, 2019)
      We study geometric properties of Krylov projection methods for large and sparse linear Hamiltonian systems. We consider in particular energy-preservation. We discuss the connection to structure preserving model reduction. ...
    • Krylovmetoder for lineære hamiltonske differensiallikninger 

      Eskeland, Sindre (Master thesis, 2016)
      Krylovmetoder er projeksjonsmetoder som kan transformere store lineære differensialligninger til mindre lineære differesialligninger med lignende egenskaper. To slike metoder (symplectic Lanczos method og Krylov projection ...
    • Learning Hamiltonians of constrained mechanical systems 

      Celledoni, Elena; Leone, Andrea; Murari, Davide; Owren, Brynjulf (Peer reviewed; Journal article, 2022)
      Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is ...
    • Lie Group integrators for mechanical systems 

      Celledoni, Elena; Çokaj, Ergys; Leone, Andrea; Murari, Davide; Owren, Brynjulf (Peer reviewed; Journal article, 2021)
      Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical ...
    • Neural Networks on Low-Rank and Stiefel Manifolds 

      Klemetsen, Camilla Balestrand (Master thesis, 2022)
      I denne oppgaven ser vi på effekten av dyp læring som optimal kontroll på mangfoldigheter. Vi utvikler og trener flere nettverk som bevarer lav-rang og ortogonalitet i treningsprosessen. Bibetingelsen til optimal kontroll ...
    • Noise removal in synthetically generated diffusion tensor imaging data using a denoising autoencoder 

      Wiik, Anders (Bachelor thesis, 2020)
      Diffusjonstensor avbildning (DTI) er en populær medisinsk avbildningsteknikk som kartlegger diffusjonen av vannmolekyler i biologisk vev. Målte DTI-data er forurenset av støy, og temaet for dette prosjektet var å utforske ...
    • A novel approach to rigid spheroid models in viscous flows using operator splitting methods 

      Tapley, Benjamin; Celledoni, Elena; Owren, Brynjulf; Andersson, Helge Ingolf (Peer reviewed; Journal article, 2019)
      Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for ...
    • Numerical integration in inverse problems for ordinary differential equations 

      Noren, Håkon (Master thesis, 2022)
      Dersom ein kjenner punkter av løysinga til ei ordinær differensiallikning (ODE), handlar det inverse problemet om å finne ein approksimasjon av vektorfeltet. Ei forskingsretning som nyleg har vorte særs aktiv, dreier seg ...
    • Numerical Methods for Nonholonomic Mechanics 

      Hilden, Sindre Kristensen (Master thesis, 2009)
      We discuss nonholonomic systems in general and numerical methods for solving them. Two different approaches for obtaining numerical methods are considered; discretization of the Lagrange-d'Alembert equations on the one ...
    • Numerical Methods for Nonholonomic Rigid Body Dynamics 

      Høiseth, Eirik Hoel (Master thesis, 2011)
      We discuss general nonholonomic systems on manifolds in the setting of both continousand discrete mechanics, before focusing on systems with symmetry that enable a reduction of the equations of motion to a quotient space ...
    • Numerical Simulation of Nonholonomic Dynamics 

      Evensberget, Dag Frohde (Master thesis, 2006)
      We study the numerical integration of nonholonomic problems. The problems are formulated using Lagrangian and Hamiltonian mechanics. We review briefly the theoretical concepts used in geometric mechanics. We reconstruct ...
    • Numerical Solution of Equilibrium Equations of Spatial Elastica 

      Ringheim, Inger Marie (Master thesis, 2013)
      The goal of the thesis was to simulate numerically some equilibrium equationsof spatial elastica, where the equations simulate an elastic rod that has been de-formed. The equations are taken from the article ?Analytical ...
    • Optimal Control of Multibody Dynamics with Applications 

      Nøst, Petter (Master thesis, 2023)
      Vi presenterer en metode for å representere bjelker ved hjelp av flerkroppsdynamikk, nærmere bestemt et system av stive ledd som kalles en pendelkjede. Ved å innføre ledd i uttrykket som straffer vinkler mellom påfølgende ...
    • Optimal reparametrization of curves in shape analysis by introducing a deep neural network architecture 

      Bærland, Hege (Master thesis, 2021)
      Former er typisk beskrecet som det som er igjen av et objekt uten å ta hensyn til plassering, rotasjon og størrelse. En stor del av formanalyse består av å definere likheter og forskjeller mellom formene for å utføre ulike ...
    • Optimization on Matrix Manifolds with Applications to Blind Source Separation 

      Kvernelv, Vegard Berg (Master thesis, 2013)
      Studere hvordan konsepter fra optimeringsteori generaliseres til mangfoldigheter, mer spesifikt matrisemangfoldigheter, og vurdere hvordan dette kan anvendes på "blind source separation"-problemer
    • Passivity-preserving splitting methods for rigid body systems 

      Celledoni, Elena; Høiseth, Eirik Hoel; Ramzina, Nataliya (Journal article, 2018)
      A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input–output passive. We ...
    • Predicting bending moments with machine learning 

      Celledoni, Elena; Gustad, Halvor Snersrud; Kopylov, Nikita; Sundklakk, Henrik Sperre (Peer reviewed; Journal article, 2019)
      We investigate the possibility of predicting the bending moment of slender structures based on a limited number of deflection measurements. These predictions can help to estimate the wear and tear of the structures. We ...
    • Rigid Body Attitude Control 

      Kleivedalen, Anne Mari (Master thesis, 2014)
      Geometric numerical integration schemes have been studied for rigid body attitudecontrol problems. We consider symplectic integrators and present a Lie group varia-tional integrator and a discrete gradient method. The two ...