CAREER: Topology-Driven Uncertainty Visualization for Scientific Ensembles

Scientific simulations are increasingly used to understand and predict complex real-world phenomena, from forecasting hurricanes to designing advanced materials and engineering systems. Rather than relying on a single simulation, scientists often run hundreds of variations, called ensemble simulations, to capture the range of possible outcomes and assess uncertainty. However, the sheer volume and complexity of these simulations make it difficult to determine which results are reliable and which remain uncertain. Without effective methods to analyze and communicate uncertainty, scientists may draw overly confident conclusions, potentially affecting decisions in areas such as weather forecasting, energy systems, and engineering design. This project develops new mathematical, computational, and visualization techniques that help scientists better understand uncertainty in large simulation ensembles, supporting more informed and trustworthy decision-making. The resulting tools will be released as open-source software for the broader scientific community and integrated into educational activities that train future data scientists and introduce K–12 students to data literacy, scientific reasoning, and uncertainty. This project advances the science of uncertainty visualization through three coordinated research efforts grounded in Topological Data Analysis (TDA), a mathematical framework that captures the structural organization of data beyond traditional statistical summaries. The first effort, TopoFeat, develops scalable methods for extracting and characterizing meaningful structural features across large simulation ensembles. The second effort, HyUQ, introduces a hybrid uncertainty quantification framework that combines mathematical modeling and machine learning to characterize, predict, and aggregate feature-level uncertainty. The third effort, VisUQ, develops an interactive visualization platform that enables scientists to explore uncertainty through coordinated visual analytics, uncertainty-aware visual representations, and domain-specific analysis tools. Together, these advances will establish a mathematically grounded framework for uncertainty-aware analysis and visualization of scientific ensembles, with applications spanning climate science, fluid dynamics, neuroscience, materials discovery, and other data-intensive scientific domains. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.