DFG-Sachbeihilfe: Efficient Quasi Monte Carlo Methods and Their Application in Quantum Field Theory

The project aims at the exploration of quasi Monte Carlo (QMC) methods for applications in Euclidean quantum field theory and statistical mechanics. We plan to explore and construct efficient effective-dimension reduction techniques based on derivative information of the underlying integrands using new techniques of algorithmic differentiation. These techniques will be used for Monte Carlo simulations of models in Euclidean lattice field theory and for the computation of so-called dis-connected diagrams. The application of new algorithmic differentiation techniques in this project pursues two different goals: First, we will explore dimension reduction techniques based on derivative information of the target integrands which will represent systems of lattice field theory with compact integration variables as needed for gauge theories and the stochastic evaluation of the discretized quark propagator. Secondly, we aim at using derivative information for an effective construction of QMC rules tailored to the target integrands. We will also apply and test the efficiency of Sobol' sequences with additional uniformity properties. It was shown by one of our collaborators that these properties provide an additional guarantee of uniformity for high-dimensional problems even at a small number of sampled points, which may be beneficial in applications to Euclidean quantum field problems. We want to extent the efficient construction and application of QMC methods and (effective) dimension reduction techniques to other classes of problems. In particular, we want to look at problems where the relevant degrees of freedom are in a compact group.

Tischendorf, Caren Prof. Dr. (Details) (Angewandte Mathematik)
Griewank, Andreas Prof. Dr. (Details) (Seniorprofessor(inn)en und Professor(inn)en im Ruhestand)

Beteiligte externe Organisationen

DFG: Sachbeihilfe

Projektstart: 01/2014
Projektende: 12/2016

Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder, Mathematik

Zuletzt aktualisiert 2022-09-09 um 01:06