Lecture

Monte Carlo Integration: Correlated Sampling

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In course

PHYS-403: Computer simulation of physical systems I

The two main topics covered by this course are classical molecular dynamics and the Monte Carlo method. ...

Description

This lecture covers Monte Carlo integration through correlated sampling, focusing on the motivation behind using this method, the integration process, and the scaling of errors. It also discusses the performance of supercomputers in this context and compares Monte Carlo methods with conventional schemes. The lecture concludes with a detailed analysis of error scaling for grid integration in multiple dimensions.

Instructor

Alfredo Pasquarello

Alfredo Pasquarello studied physics at the Scuola Normale Superiore of Pisa and at the University of Pisa, obtaining their respective degrees in 1986. He obtained a doctoral degree at the EPFL in 1991 with a thesis on Multiphoton Transitions in Solids . Then, he moved to Bell Laboratories at Murray Hill (New Jersey), where he carried out postdoctoral research on the magnetic properties of carbon fullerenes. In 1993, he joined the Institute for Numerical Research in the Physics of Materials (IRRMA), where his activity involved first-principles simulation methods. In 1998, he was awarded the EPFL Latsis Prize for his research work on disordered silica materials. Succeeding in grant programs of the Swiss National Science Foundation, he then set up his own research group at IRRMA. In July 2003, he is appointed Professor in Theoretical Condensed Matter Physics at EPFL. Currently, he leads the Chair of Atomic Scale Simulation.

Official source

Related concepts (32)

Supercomputer

A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2017, there have existed supercomputers which can perform over 1017 FLOPS (a hundred quadrillion FLOPS, 100 petaFLOPS or 100 PFLOPS). For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013).

Roadrunner (supercomputer)

Roadrunner was a supercomputer built by IBM for the Los Alamos National Laboratory in New Mexico, USA. The US$100-million Roadrunner was designed for a peak performance of 1.7 petaflops. It achieved 1.026 petaflops on May 25, 2008, to become the world's first TOP500 LINPACK sustained 1.0 petaflops system. In November 2008, it reached a top performance of 1.456 petaFLOPS, retaining its top spot in the TOP500 list. It was also the fourth-most energy-efficient supercomputer in the world on the Supermicro Green500 list, with an operational rate of 444.

Titan (supercomputer)

Titan or OLCF-3 was a supercomputer built by Cray at Oak Ridge National Laboratory for use in a variety of science projects. Titan was an upgrade of Jaguar, a previous supercomputer at Oak Ridge, that uses graphics processing units (GPUs) in addition to conventional central processing units (CPUs). Titan was the first such hybrid to perform over 10 petaFLOPS. The upgrade began in October 2011, commenced stability testing in October 2012 and it became available to researchers in early 2013.

TOP500

The TOP500 project ranks and details the 500 most powerful non-distributed computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year. The first of these updates always coincides with the International Supercomputing Conference in June, and the second is presented at the ACM/IEEE Supercomputing Conference in November.

Gibbs sampling

In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables).

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