Sökning: "Tensors"

Visar resultat 1 - 5 av 30 uppsatser innehållade ordet Tensors.

1. 1. Estimating Diffusion Tensor Distributions With Neural Networks

   Master-uppsats, Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

   Författare :Rimaz Nismi; [2024]
   Nyckelord :Diffusion; Magnetic Resonance Imaging; MRI; Neural Networks; Optimal transport; Earth mover s distance; Sinkhorn distance;

   Sammanfattning : Magnetic Resonance Imaging (MRI) is an essential healthcare technology, with diffusion MRI being a specialized technique. Diffusion MRI exploits the inherent diffusion of water molecules within the human body to produce a high-resolution tissue image. An MRI image contains information about a 3D volume in space, composed of 3D units called voxels. LÄS MER

3. 2. Analysis and optimization of an implementation of hierarchical Tucker tensors

   Kandidat-uppsats, Uppsala universitet/Institutionen för informationsteknologi

   Författare :Daniel Wallgren; [2023]
   Nyckelord :;

   Sammanfattning : The hierarchical Tucker tensor format is a format for approximated tensors which has been decomposed into smaller parts. This structure can be useful in high-dimensional computer simulations. One implementation of this structure is in a library called htlib. LÄS MER

4. 3. A Hierarchical Tucker Solver for the Vlasov-Maxwell System

   Master-uppsats, Uppsala universitet/Institutionen för informationsteknologi

   Författare :Oskar Tegby; [2023]
   Nyckelord :;

   Sammanfattning : The Vlasov-Maxwell equations is a common model to describe the behavior of a plasma, but come at the cost of their dimensionality since both spatial and veloocity data is stored in three dimensions. This causes a significant obstacle to be able solve them numerically since the size of the data is N^6, which yields a data size of 8. LÄS MER

5. 4. Tensor rank and support rank in the context of algebraic complexity theory

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Pelle Andersson; [2023]
   Nyckelord :linear algebra; tensor product; tensor rank; matrix multiplication; complexity; linjär algebra; tensorprodukt; tensorrang; matrismultiplikation; komplexitet;

   Sammanfattning : Starting with the work of Volker Strassen, algorithms for matrix multiplication have been developed which are time complexity-wise more efficient than the standard algorithm from the definition of multiplication. The general method of the developments has been viewing the bilinear mapping that matrix multiplication is as a three-dimensional tensor, where there is an exact correspondence between time complexity of the multiplication algorithm and tensor rank. LÄS MER

7. 5. Multi-Scale Topology Optimization of Lattice Structures Using Machine Learning

   Uppsats för yrkesexamina på avancerad nivå, Uppsala universitet/Tillämpad mekanik

   Författare :Julia Ibstedt; [2023]
   Nyckelord :Topology optimization; Multi-scale topology optimization; Machine learning; Gaussian process; Homogenization; Inverse homogenization; Anisotropic materials; Symmetry groups; Material property space; Topologioptimering; Flerskalig topologioptimering; Maskininlärning; Gaussian process; Homogenisering; Anisotropa material; Symmetrigrupper; Materialegenskapsrymd;

   Sammanfattning : This thesis explores using multi-scale topology optimization (TO) by utilizing inverse homogenization to automate the adjustment of each unit-cell's geometry and placement in a lattice structure within a pressure vessel (the design domain) to achieve desired structural properties. The aim is to find the optimal material distribution within the design domain as well as desired material properties at each discretized element and use machine learning (ML) to map microstructures with corresponding prescribed effective properties. LÄS MER