GPU-Based Parallel Search of Relevant Variable Sets in Complex Systems

Various methods have been proposed to identify emergent dynamical structures in complex systems. In this paper, we focus on the Dynamical Cluster Index (DCI), a measure based on information theory which allows one to detect relevant sets, i. e. sets of variables that behave in a coherent and coordinated way while loosely interacting with the rest of the system. The method associates a score to each subset of system variables; therefore, for a thorough analysis of the system, it requires an exhaustive enumeration of all possible subsets. For large systems, the curse of dimensionality makes the problem solvable only using metaheuristics. Even within such approaches, however, DCI computation has to be performed for a huge number of times; thus, an efficient implementation becomes a mandatory requirement. Considering that a candidate relevant set's DCI can be computed independently of the others, we propose a GPU-based massively parallel implementation of DCI computation. We describe the algorithm's structure and validate it by assessing the speedup in comparison with a single-thread sequential CPU implementation when analyzing a set of dynamical systems of different sizes.