In this paper, we study the propagation of data uncertainty through the marching cubes algorithm for isosurface visualization for correlated uncertain data. Consideration of correlation has been shown paramount for avoiding errors in uncertainty quantification and visualization in multiple prior studies. Although the problem of isosurface uncertainty with spatial data correlation has been previously addressed, there are two major limitations to prior treatments. First, there are no analytical formulations for uncertainty quantification of isosurfaces when the data uncertainty is characterized by a Gaussian distribution with spatial correlation. Second, as a consequence of the lack of analytical formulations, existing techniques resort to a Monte Carlo sampling approach, which is expensive and difficult to integrate into visualization tools. To address these limitations, we present a closed-form framework to efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the Hinkley's derivation on the ratio of Gaussian distributions. With our analytical framework, we achieve a significant speed-up and enhanced accuracy of uncertainty quantification over classical Monte Carlo methods. We further accelerate our analytical solutions using many-core processors to achieve speed-ups up to $\text{585} \times$585× and integrability with production visualization tools for broader impact. We demonstrate the effectiveness of our correlation-aware uncertainty framework through experiments on meteorology, urban flow, and astrophysics simulation datasets.

Resolving the most fundamental questions in cosmology requires simulations that match the scale, fidelity, and physical complexity demanded by next-generation sky surveys. To achieve the realism needed for this critical scientific partnership, detailed gas dynamics must be treated self-consistently with gravity for end-to-end modeling of structure formation. Exascale computing enables simulations that span survey-scale volumes while incorporating key astrophysical processes that shape complex cosmic structures. We present results from CRK-HACC, a cosmological hydrodynamics code built for extreme scalability. Using separation-of-scale techniques, GPU-resident tree solvers, in situ analysis pipelines, and multi-tiered I/O, CRK-HACCexecuted Frontier-E: a four trillion particle full-sky simulation, over an order of magnitude larger than previous efforts. The run achieved 513.1 PFLOPs peak performance, processing 46.6 billion particles per second and writing more than 100 PB of data in just over one week of runtime. Frontier-E marks a significant advance in predictive modeling for next-generation cosmological science.

As the US Department of Energy (DOE) computing facilities began deploying petascale systems in 2008, DOE was already setting its sights on exascale. In that year, DARPA published a report on the feasibility of reaching exascale. The report authors identified several key challenges in the pursuit of exascale including power, memory, concurrency, and resiliency. That report informed the DOE's computing strategy for reaching exascale. With the deployment of Oak Ridge National Laboratory's Frontier supercomputer, we have officially entered the exascale era. In this paper, we discuss Frontier's architecture, how it addresses those challenges, and describe some early application results from Oak Ridge Leadership Computing Facility's Center of Excellence and the Exascale Computing Project.

The advent of Exascale computing invites an assessment of existing best practices for developing application readiness on the world's largest supercomputers. This work details observations from the last four years in preparing scientific applications to run on the Oak Ridge Leadership Computing Facility's (OLCF) Frontier system. This paper addresses a range of topics in software including programmability, tuning, and portability considerations that are key to moving applications from existing systems to future installations. A set of representative workloads provides case studies for general system and software testing. We evaluate the use of early access systems for development across several generations of hardware. Finally, we discuss how best practices were identified and disseminated to the community through a wide range of activities including user-guides and trainings. We conclude with recommendations for ensuring application readiness on future leadership computing systems.