Publication Date
Spring 3-29-2023
Abstract
For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as well as improve stability for the time-stepping on coarser levels.
Degree Name
Mathematics
Level of Degree
Masters
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Jehanzeb H Chaudhary
Second Committee Member
Jacob B Schroder
Third Committee Member
Stephen Lau
Language
English
Keywords
multigrid parallel-in-time MGRIT PINNs DNNs
Document Type
Thesis
Recommended Citation
Gutierrez, Jonathan P.. "Using Physics-Informed Neural Networks for Multigrid in Time Coarse Grid Equations." (2023). https://digitalrepository.unm.edu/math_etds/200
