Topology-Based Visualization Techniques for Scientific Data Exploration.

Data visualization provides intuitive and practical tools for information exploration and scientific discovery. However, with the increased availability of computing resources and sensing devices, data's ever-increasing size and complexity pose fundamental challenges to existing visualization techniques. The first challenge is data understanding, requiring new methodologies to extract key features and insights from large-scale data. Second, the development of data transmission and storage systems is outpaced by unprecedented data growth. This disparity challenges in situ data processing since data need to be transferred to a commodity workstation to conduct interactive inspections. Third, visualization tools and methodologies for understanding the uncertainties of scientific simulations are lacking. The author's research aims to address these challenges by significantly enriching topology-based visualization methodologies and tools for scientific data exploration. The author's dissertation (Yan, 2022) made advances in three areas: redefining topology for domain-specific features for data understanding, enhancing data reduction with topology for data transmission and storage, and developing methodologies for statistical feature analysis to mitigate uncertainty in data visualization. These methodologies and tools have applications in structural biology, climate science, combustion study, and neuroscience.