Shared-Memory Parallel Computation of Morse-Smale Complexes with Improved Accuracy

Abstract

Topological techniques have proven to be a powerful tool in the analysis and visualization of large-scale scientific data. In particular, the Morse-Smale complex and its various components provide a rich framework for robust feature definition and computation. Consequently, there now exist a number of approaches to compute Morse-Smale complexes for large-scale data in parallel. However, existing techniques are based on discrete concepts which produce the correct topological structure but are known to introduce grid artifacts in the resulting geometry. Here, we present a new approach that combines parallel streamline computation with combinatorial methods to construct a high-quality discrete Morse-Smale complex. In addition to being invariant to the orientation of the underlying grid, this algorithm allows users to selectively build a subset of features using high-quality geometry. In particular, a user may specifically select which ascending/descending manifolds are reconstructed with improved accuracy, focusing computational effort where it matters for subsequent analysis. This approach computes Morse-Smale complexes for larger data than previously feasible with significant speedups. We demonstrate and validate our approach using several examples from a variety of different scientific domains, and evaluate the performance of our method.

GPU Parallel Computation of Morse-Smale Complexes

“…We ensure identical parameters when comparing our results with [23,24]. The results reported by Gyulassy et al [14,15,17] and Bhatia et al [6] focus on improving geometric accuracy, thus yielding larger runtimes.…”

“…However, the best known algorithms for the more complex saddle-saddle traversals are still variants of a fast serial breadth first search traversal. More recently, Gyulassy et al [14,15,17] and Bhatia et al [6] have presented methods that ensure accurate geometry while computing the 3D MS complex in parallel. The approaches described above, with the exception of Shivashankar and Natarajan [23], implement CPU based shared memory parallelization strategies.…”

Priority research directions for in situ data management: Enabling scientific discovery from diverse data sources

“…In situ analysis algorithms may transform data into reduced representations or surrogate models in order to mitigate large data size, high dimensionality, or long computation times. Low-rank approximation (Austin et al, 2016), statistical summarization (Biswas et al, 2018;Dutta et al, 2017;Hazarika et al, 2018;Lawrence et al, 2017;Lohrmann et al, 2017;Thompson et al, 2011), topological segmentation (Gyulassy et al, 2012(Gyulassy et al, , 2019Landge et al, 2014;Weber, 2013, 2014), wavelet transformation (Li et al, 2017;Salloum et al, 2018), lossy compression (Brislawn et al, 2012;Di and Cappello, 2016;Lindstrom, 2014), geometric modeling (Nashed et al, 2019; Peterka et al, 2018), and feature detection (Guo et al, 2017) may be used to generate reduced or surrogate models.…”

“…Research is required to modify existing post hoc algorithms and develop new in situ algorithms to satisfy the needs of modern use cases on emerging system architectures that can feature massive scale, many cores, deep memory hierarchies, or embedded lightweight edge devices. Examples of such algorithms include reduced representations and low-rank approximations (Austin et al, 2016), statistical (Biswas et al, 2018;Dutta et al, 2017;Hazarika et al, 2018;Thompson et al, 2011), topological (Gyulassy et al, 2012(Gyulassy et al, , 2019Landge et al, 2014;Weber, 2013, 2014), wavelets (Li et al, 2017;Salloum et al, 2018), compression (Brislawn et al, 2012;Di and Cappello, 2016;Lindstrom, 2014), and feature detection (Guo et al, 2017) methods. Surrogate models and multifidelity models can be geometric (Nashed et al, 2019;Peterka et al, 2018), statistical (Lawrence et al, 2017;Lohrmann et al, 2017), or neural network (He et al, 2019).…”

Progressive Wasserstein Barycenters of Persistence Diagrams

“…Moreover, to distinguish noise from features, concepts from Persistent Homology [27,29] provide importance measures, which are both theoretically well established and meaningful in the applications. Among the existing abstractions, such as contour trees [19], Reeb graphs [16,66,93], or Morse-Smale complexes [25,40,41,43], the persistence diagram [29] has been extensively studied. In particular, its conciseness, stability [22] and expressiveness make it an appealing candidate for data summarization tasks.…”