Multiscale Morse theory for science discovery

Abstract

Computational scientists employ increasingly powerful parallel supercomputers to model and simulate fundamental physical phenomena. These simulations typically produce massive amounts of data easily running into terabytes and petabytes in the near future. The future ability of scientists to analyze such data, validate their models, and understand the physics depends on the development of new mathematical frameworks and software tools that can tackle this unprecedented complexity in feature characterization and extraction problems. We present recent advances in Morse theory and its use in the development of robust data analysis tools. We demonstrate its practical use in the analysis of two large scale scientific simulations: (i) a direct numerical simulation and a large eddy simulation of the mixing layer in a hydrodynamic instability and (ii) an atomistic simulation of a porous medium under impact. Our ability to perform these two fundamentally different analyses using the same mathematical framework of Morse theory demonstrates the flexibility of our approach and its robustness in managing massive models.