Michalak, Sarah E. | Search NASA

DOE OSTI2016

Spatiotemporal modeling of node temperatures in supercomputers

Los Alamos National Laboratory (LANL) is home to many large supercomputing clusters. These clusters require an enormous amount of power (~500-2000 kW each), and most of this energy is converted into heat. Thus, cooling the components of the supercomputer becomes a critical and expensive endeavor. Recently a project was initiated to investigate the effect that changes to the cooling system in a machine room had on three large machines that were housed there. Coupled with this goal was the aim to develop a general good-practice for characterizing the effect of cooling changes and monitoring machine node temperatures in this and other machine rooms. This paper focuses on the statistical approach used to quantify the effect that several cooling changes to the room had on the temperatures of the individual nodes of the computers. The largest cluster in the room has 1,600 nodes that run a variety of jobs during general use. Since extremes temperatures are important, a Normal distribution plus generalized Pareto distribution for the upper tail is used to model the marginal distribution, along with a Gaussian process copula to account for spatio-temporal dependence. A Gaussian Markov random field (GMRF) model is used to model the spatial effects on the node temperatures as the cooling changes take place. This model is then used to assess the condition of the node temperatures after each change to the room. The analysis approach was used to uncover the cause of a problematic episode of overheating nodes on one of the supercomputing clusters. Lastly, this same approach can easily be applied to monitor and investigate cooling systems at other data centers, as well.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Posterior propriety for hierarchical models with log-likelihoods that have norm bounds

Statisticians often use improper priors to express ignorance or to provide good frequency properties, requiring that posterior propriety be verified. Our paper addresses generalized linear mixed models, GLMMs, when Level I parameters have Normal distributions, with many commonly-used hyperpriors. It provides easy-to-verify sufficient posterior propriety conditions based on dimensions, matrix ranks, and exponentiated norm bounds, ENBs, for the Level I likelihood. Since many familiar likelihoods have ENBs, which is often verifiable via log-concavity and MLE finiteness, our novel use of ENBs permits unification of posterior propriety results and posterior MGF/moment results for many useful Level I distributions, including those commonly used with multilevel generalized linear models, e.g., GLMMs and hierarchical generalized linear models, HGLMs. Furthermore, those who need to verify existence of posterior distributions or of posterior MGFs/moments for a multilevel generalized linear model given a proper or improper multivariate F prior as in Section 1 should find the required results in Sections 1 and 2 and Theorem 3 (GLMMs), Theorem 4 (HGLMs), or Theorem 5 (posterior MGFs/moments).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Randomized selection on the GPU

We implement here a fast and memory-sparing probabilistic top k selection algorithm on the GPU. The algorithm proceeds via an iterative probabilistic guess-and-check process on pivots for a three-way partition. When the guess is correct, the problem is reduced to selection on a much smaller set. This probabilistic algorithm always gives a correct result and always terminates. Las Vegas algorithms of this kind are a form of stochastic optimization and can be well suited to more general parallel processors with limited amounts of fast memory.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2011

Randomized selection on the GPU

We implement here a fast and memory-sparing probabilistic top k selection algorithm on the GPU. The algorithm proceeds via an iterative probabilistic guess-and-check process on pivots for a three-way partition. When the guess is correct, the problem is reduced to selection on a much smaller set. This probabilistic algorithm always gives a correct result and always terminates. Las Vegas algorithms of this kind are a form of stochastic optimization and can be well suited to more general parallel processors with limited amounts of fast memory.

99 GENERAL AND MISCELLANEOUS↗