What kinds of problems are suitable to be solved by desktop grid environment? Alexander Afanasyev The Institute for Information Transmission Problems (Kharkevich Institute) RAS Moscow BOINC:FAST’2015 Petrozavodsk, Russia, September 14-18, 2015

Supercoputers Grids and Clouds Desktop grid

DEGISCO WP4 29/09/ For which tasks are GSPC? A large amount of calculations (a few days of calculations on a PC and more). Weakly-related tasks (problem is decomposed into independent parts that do not require interaction in the process of calculations ).

Tasks combinatorial and global optimization

Applications Combinatorics Cryptanalysis of ciphers Search Latin squares Test mathematical hypotheses Verification Optimization Docking proteins The analysis of the spatial configuration of chemical compounds Identification of model parameters

DEGISCO WP4 29/09/ the Most successful project of GSPC in Russia The project is a research project aimed at solving complex scientific problems reducible to the problem of inversion of Boolean functions Peak performance of 10 TFlops ESTO RAS IITP

Search configuration of atoms with a minimum of interaction energy - the distance between atoms i and j - the pair potential ; - the potential of a Lennard Jones; - the Morse potential.

The organization of calculations in the BOINC environment Selection variants and generation of new jobs The server clients

The results of the experiment The problem of finding the minimum of the cluster with the Morse potential (rho = 14), 150 atoms has been solved. There were able to get the minimum value in 10 days calculations. The result corresponds to the best found so far value using a geometrically-based methods. The improved results obtained previously using the methods of General use.

Potential Tersoff Cohesive energy E coh of a system of atoms - the potential energy of interaction between two particles i and j, where - cutoff-fnction, Members are responsible for the repulsion and attraction: Multi-particle interaction parameter

The objective function for the optimization problem For regular repeating lattice of atoms to measure a number of parameters with the potential Tersoff: -cohesive energy, elastic constants The objective function is written as follows, where - free potential parameters Tersoff

The results of the experiment 3 days calculation

The method of branches and borders TREE BRANCHBRANCHING SUBPROBLEM OUT SUBPROBLEM: 1. HAS NO SOLUTIONS 2. THE OPTIMUM WAS FOUND 3. THE OPTIMUM IS NOT BETTER THAN PREVIOUSLY FOUND (RECORD )

The scope of application of the method of branches and borders Method of branches and borders lies at the heart of many deterministic optimization algorithms Deterministic methods guarantee the accuracy of the solutions and are used in the solution of problems where this guarantee is essential

Method of branches and boundaries for GSPC The main problem is different, unknown in advance, the complexity of the subproblems. Therefore, an efficient distributed implementation is more complicated than in the case of iterative algorithms. Require load balancing, which in the case of GSPC is reduced to the proper formation of computational units, taking into account a priori estimates of the complexity of the subproblems.

The problem arises in the analysis of carbon nanostructures that arise in the form of deposits on the walls of tokamaks. The tokamak (toroidal chamber with magnetic coils) is the toroidal unit for magnetic confinement of plasma to achieve the conditions necessary for the flow of controlled thermonuclear fusion. The analysis of these structures is a typical big data problem.

17 L2 optimization R=1 nm, Rx=0.3 nm, Ry=0.5 nm R=1.05 nm, Rx=0.3 nm, Ry=0.5 nm R=1.1 nm, Rx=0.3 nm, Ry=0.5 nm R=0.95 nm, Rx=0.3 nm, Ry=0.6 nm R=1 nm, Rx=0.3 nm, Ry=0.6 nm R=1.2 nm, Rx=0.3 nm, Ry=0.65 nm Atoms: CHCr, Fe, NiNb, MoTl Chemical contents of amorphous medium taken from experiment Structural analysis of carbon films. The mixture of structures.

18 Визуализация результатов Суммарный график

Supercoputers Grids and Clouds Desktop grid

MathCloud: Architecture

Cauchy problem for differential equations with polynomial right-hand sides Where - n-dimensional polynomial m-th order with constant coefficients.

Quasi-symbolic representation of the approximate solution of the Cauchy problem for systems of ordinary differential equations with polynomial right-hand sides in the form of a segment of a Taylor series n - the order of system control m - degree polynomial right-hand side of the multidimensional control i - the serial number of the polynomial T x0 in the Taylor series expansion (Ti (x0)) im-i +1 - the degree of Ti (x0) nim-i +2 - the number of coefficients in the i-th term of the Taylor expansion i - number of expansion terms

Lorenz System under standart parameters σ =10, r=28,b =8/3

crunchers corporative computing computers crowdsourcing

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Технологии ГСПК BOINC (Berkeley Open Infrastructure for Network Computing) OurGrid XtremWeb-HEP (XWHEP)

BOINC (Berkeley Open Infrastructure for Network Computing) Самая популярная платформа для добровольных вычислений Поддерживается всеми видами OS и Android Средняя суммарная реальная производительность всех BOINC-проектов на примерно 18 PetaFLOPS (по данным

Collatz’ Conjecture Tests the Collatz conjecture the Collatz Conjecture (hypothesis 3n+1, the hypothesis 3x+1, of Collatz problem, the problem of 3n+1, the problem 3x+1, Syracuse problem) is one of the unsolved problems of mathematics, named after the German mathematician Lothar Collatz (English), who proposed it in The average performance of 2.5 PFlops (according to

The solution of combinatorial problems in project is a research project that uses connected via the Internet of computers to solve hard and practically important problems (discrete functions, discrete optimization, bioinformatics, etc.) that can be effectively reduced to the problem of satisfiability of Boolean formulas. At this point in the project is analyzed cipher Bivium (a weakened version of the cipher Trivium). Peak performance of 10 TFlops. An average of 1,000 active hosts from connected to the project.

Алгоритм решения: псевдо-локальный поиск

Алгоритм решения: глобализация Улучшение Отбор лучших

Компоненты приложения Сервер Клиент Скрипт, осуществляющий генерацию новых заданий и обработку полученных (periodic task) Программа, осуществляющая полу-локальный поиск, интегрированная с boinc- wrapper.

Задачи идентификации параметров модели