Talha bin Masood: Topology-based methods in Scientific data analysis and visualization

Abstract

Modern scientific research is progressively centered around data, with large-scale simulations generating large and complex data sets represented as scalar, vector, or tensor fields over spatial domains. High-resolution imaging devices and sensors are another important source of similarly rich data. However, data alone lacks utility without insights. There is a pressing need for efficient analysis methods to extract meaningful insights from such data. Scientific visualization research aims to address this challenge by developing novel data analysis methods and interactive visualization techniques to assist domain scientists in the discovery process.

A key task in this context is identifying and extracting features, i.e. hidden substructures in the data, which vary based on the application (e.g., vortices in fluid simulations, binding sites in molecular dynamics, cyclones in climate simulations, brain fiber tracts in diffusion tensor imaging, etc). Topological data analysis (TDA) is increasingly employed to provide a mathematically robust foundation for features and their extraction. TDA offers powerful tools, including multi-scale methods that preserve essential features and eliminate noise. In this talk, I will give a few examples demonstrating how topological abstractions such as merge trees and Morse-Smale complexes have been used successfully for data analysis and visualization in different application contexts. I will also talk about the current challenges and open questions in feature-driven scientific visualization, particularly related to feature comparison where TDA methods can provide robust solutions.