Sökning: "differential operator"

Visar resultat 1 - 5 av 25 uppsatser innehållade orden differential operator.

1. 1. A type-driven approach for sensitivity checking with branching

   Master-uppsats, Göteborgs universitet/Institutionen för data- och informationsteknik

   Författare :Daniel Freiermuth; [2023-10-24]
   Nyckelord :Computer; science; computer science; thesis; differential privacy; type system; sensitivity; branching;

   Sammanfattning : Differential Privacy (DP) is a promising approach to allow privacy preserving statistics over large datasets of sensitive data. It works by adding random noise to the result of the analytics. Understanding the sensitivity of a query is key to add the right amount of noise capable of protecting privacy of individuals in the dataset. LÄS MER

3. 2. Gravity water waves over constant vorticity flows: from laminar flows to touching waves

   Master-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Författare :Francisco Gonçalves Jorge Dias de Carvalho; [2023]
   Nyckelord :Partial differential equations; Water waves; Euler equations; Free boundary problem; Bifurcation theory; Nonlinear functional analysis; Hilbert transform; Mathematics and Statistics;

   Sammanfattning : In a recent paper, Hur and Wheeler proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow and subject to gravity whose profile overhangs, among which, waves whose surface touches at a point, enclosing a bubble of air. We take this further, proving the existence of a continuous curve of water waves from a laminar flow up to a touching wave for fixed non-zero gravity. LÄS MER

4. 3. Deep learning of nonlinear development of unstable flame fronts

   Master-uppsats, Lunds universitet/Institutionen för energivetenskaper

   Författare :Ludvig Nobel; [2023]
   Nyckelord :Technology and Engineering;

   Sammanfattning : The purpose of this study is to investigate Machine Learning methods and their ability to learn the development of nonlinear unstable flame fronts due to diffusive-thermal instabilities. This task is performed by first numerically computing long time-sequences of solutions to the chaotic partial differential equation named Kuramoto-Sivashinsky equation which models such instabilities in a flame front. LÄS MER

5. 4. Solving Partial Differential Equations With Neural Networks

   Master-uppsats, Uppsala universitet/Matematiska institutionen

   Författare :Håkan Karlsson Faronius; [2023]
   Nyckelord :Partial differential equations; neural networks; physics-informed neural networks; deep ritz method; fourier neural operator; importance sampling; inverse problems;

   Sammanfattning : In this thesis three different approaches for solving partial differential equa-tions with neural networks will be explored; namely Physics-Informed NeuralNetworks, Fourier Neural Operators and the Deep Ritz method. Physics-Informed Neural Networks and the Deep Ritz Method are unsupervised machine learning methods, while the Fourier Neural Operator is a supervised method. LÄS MER

7. 5. Implementation and study of boundary integral operators related to PDE:s in the plane

   Master-uppsats, Lunds universitet/Matematik LTH

   Författare :Erik Andersson; [2023]
   Nyckelord :Boundary integral equation; Singular integral operator; Product integration; Close evaluation; Numerical integration; MATLAB; Mathematics and Statistics;

   Sammanfattning : The method of solving boundary value problems of partial differential equations numerically by first reformulating the problem as a boundary integral equation has many advantages over other methods, but also some unique difficulties. Some of these difficulties stem from problems in evaluating singular or nearly singular integral operators, and solving these difficulties is an active field of research. LÄS MER