A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the order of billions of unknowns. That work led to an extremely parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This paper reports on a a campaign of performance tuning and scalability studies using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were parallelized using OpenMP, and a test using 10^7 particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using SIMD instructions resulted in 4x speed-up of the overall algorithm on single-core tests with 10^3 - 10^7 particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 10^8 particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2x faster). The weak scaling test used 10^6 particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that FMM is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape

A Bayesian alternative to mutual information for the hierarchical clustering of dependent random variables

The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering

Personalizing gesture recognition using hierarchical bayesian neural networks

Building robust classifiers trained on data susceptible to group or subject-specific variations is a challenging pattern recognition problem. We develop hierarchical Bayesian neural networks to capture subject-specific variations and share statistical strength across subjects. Leveraging recent work on learning Bayesian neural networks, we build fast, scalable algorithms for inferring the posterior distribution over all network weights in the hierarchy. We also develop methods for adapting our model to new subjects when a small number of subject-specific personalization data is available. Finally, we investigate active learning algorithms for interactively labeling personalization data in resource-constrained scenarios. Focusing on the problem of gesture recognition where inter-subject variations are commonplace, we demonstrate the effectiveness of our proposed techniques. We test our framework on three widely used gesture recognition datasets, achieving personalization performance competitive with the state-of-the-art.http://openaccess.thecvf.com/content_cvpr_2017/html/Joshi_Personalizing_Gesture_Recognition_CVPR_2017_paper.htmlhttp://openaccess.thecvf.com/content_cvpr_2017/html/Joshi_Personalizing_Gesture_Recognition_CVPR_2017_paper.htmlhttp://openaccess.thecvf.com/content_cvpr_2017/html/Joshi_Personalizing_Gesture_Recognition_CVPR_2017_paper.htmlPublished versio

Direct N-body Simulations

Special high-accuracy direct force summation N-body algorithms and their relevance for the simulation of the dynamical evolution of star clusters and other gravitating N-body systems in astrophysics are presented, explained and compared with other methods. Other methods means here approximate physical models based on the Fokker-Planck equation as well as other, approximate algorithms to compute the gravitational potential in N-body systems. Questions regarding the parallel implementation of direct ``brute force'' N-body codes are discussed. The astrophysical application of the models to the theory of relaxing rotating and non-rotating collisional star clusters is presented, briefly mentioning the questions of the validity of the Fokker-Planck approximation, the existence of gravothermal oscillations and of rotation and primordial binaries.Comment: 32 pages, 13 figures, in press in Riffert, H., Werner K. (eds), Computational Astrophysics, The Journal of Computational and Applied Mathematics (JCAM), Elsevier Press, Amsterdam, 199