AVU-GSR Gaia Mission A hybrid solution for HPC and Grid-MPI infrastructures M. Bandieramonte (1,2) U. Becciani (2) Dept. of Physics and Astronomy, University of Catania (1) Astrophysics Observatory, INAF (2) , Catania, Italy Email: {marilena.bandieramonte, ugo.becciani}@oact.inaf.it A. Vecchiato, M. Lattanzi and B. Bucciarelli Astrophysics Observatory - INAF Torino, Italy Email: {vecchiato, lattanzi, bucciarelli}@oato.inaf.it Abstract—Gaia is an ambitious space mission of the European Space Agency which will chart a three-dimensional map the Milky Way to study the composition formation and evolution of our Galaxy. Our research team is developing the AVU-GSR verification module, aiming to obtain a reconstruction of the celestial sphere using a subset of GAIA observations. The authors propose a hybrid solution for HPC and Grid-MPI infrastructures which utilizes a modified LSQR – a conjugate gradient-based algorithm – to solve the system of equations for the sphere recostruction. The proposed solution has been selected as pilot test for porting HPC applications in Grid. Index Terms—LSQR; sparse linear matrix; Grid; HPC I. I NTRODUCTION Gaia is an ESA (European Space Agency) cornerstone mission, expected to be launched in mid-2013. The main goal of this mission is the production of a 5-parameters astrometric catalog (i.e. including positions, parallaxes and the two components of the proper motions) at the μarcsecond-level for about 1 billion stars of our Galaxy, by means of high- precision astrometric measurements conducted by a satellite sweeping continuously the celestial sphere during its 5-year mission. From a mathematical point of view, the satellite observations translate into a large number of equations, lin- earized with respect to the unknown parameters around known initial values, while the catalog production, which is called Global Sphere Reconstruction, requires the solution of the resulting linear system. The number of observations is much larger than that of the unknowns, so that the solution of the system in the least-squares sense eventually provides the catalog with its errors. In the Gaia mission these tasks are done by the Astrometric Global Iterative Solution (AGIS) but, given the absolute character of these results, the DPAC (Data Processing and Analysis Consortium, i.e. the international consortium which is in charge of the reduction of the Gaia data) decided to prepare a verification module which produces an independent sphere reconstruction using a subset of the Gaia observations. This is called AVU-GSR. The proposed application is for the development and testing of the part of the AVU-GSR software (Astrometric Verification Unit - Global Sphere Reconstruction) which is most demanding in terms of computational resources and at the same time most complex from the point of view of a parallelized problem. The uniqueness of the problem stands on several factors, the main being the system dimensions which are of the order of 10 10 × 10 8 . A brute-force solution of such system would take about 10 27 FLOPs, a requirement which cannot be decreased at acceptable levels even taking into account the sparsity ratio of the reduced normal matrix, which is of the order of 10 -6 . It is therefore necessary to resort to iterative algorithms. By using additional hypotheses on the correlations among the unknowns which are reflected on the convergence properties of the system, AGIS implements a block-iterative adjustment of the astrometric, attitude, instrument calibration, and global parameters, allowing the use of an embarrassingly parallel algorithm. The starting hypotheses, however, can hardly be proved rigorously, and have only been verified “a posteriori” by comparing the results with simulated true values - a situation which cannot hold in the operational phase with real data. Moreover, such method does not provide the analytical covariance between the different types of unknowns, which constitute another unique characteristic of this problem. These considerations lead to the choice of an independent approach as the one adopted by AVU-GSR, which uses a modified LSQR – a conjugate gradient-based algorithm – to solve the system of equations. In its baseline configuration, AVU-GSR is meant to handle a more limited set of stars and observations than the one treated by AGIS. The paper is organized as follows: section II illustrates the adopted solution for the parallelization of the Sphere Reconstruction problem; section III describes the data model and parallelization techniques; sections IV and V present a few results on the performance of the proposed solution and some discussions on the porting on Grid-MPI infrastructures, respectively; finally, conclusions and future works are given in section VI. II. THE SYSTEM OF EQUATIONS OF THE SPHERE RECONSTRUCTION AND ITS SOLUTION ALGORITHM The goal of AVU-GSR is to produce a Global Sphere Reconstruction using a subset of the Gaia observations. We employed a modified version of the PPN-RAMOD model used in [1] in which: • space-time is represented by the PPN approximation of the Schwarzschild metric of the Sun; : 2012 IEEE 21st International WETICE 1524-4547/12 $26.00 © 2012 IEEE DOI 10.1109/WETICE.2012.66 167 2012 IEEE 21st International WETICE 1524-4547/12 $26.00 © 2012 IEEE DOI 10.1109/WETICE.2012.66 167 2012 IEEE 21st International WETICE 1524-4547/12 $26.00 © 2012 IEEE DOI 10.1109/WETICE.2012.66 167