July 20th (Wed)

Place 名古屋大学工学部3号館273号室
contact Center for Computational Science

Time 15:00-
Rachel Levanger
Rutgers University
Using persistent homology and diffusion map embeddings to study turbulent combustion dynamics
In this talk, we will introduced two tools that can be used together to study simulated combustion dynamics. The first tool is persistent homology, a dimension reduction technique that encodes the relationship of critical points of a scalar field (local minima, maxima, and saddle points) into the Euclidean plane. The output of this `topological transformation' is called a persistence diagram, and the space of all persistence diagrams is a metric space. The second tool we use are diffusion maps, which are used to map point clouds in high-dimensional metric spaces to lower-dimensional representations that preserve local distance relations. Specifically, we will show how persistent homology and diffusion maps can be used together to study the topological characteristics of dynamics related to certain numerical quantities, e.g. enstrophy and higher-order statistics.