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Re: Monte Carlo Simulation Experiences

• To: mathgroup at smc.vnet.net
• Subject: [mg53738] Re: Monte Carlo Simulation Experiences
• From: Simon Anders <simon.anders at uibk.ac.at>
• Date: Wed, 26 Jan 2005 04:36:10 -0500 (EST)
• Organization: University of Innsbruck, Austria
• References: <cst5g5$k0n$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Mike,

MikeK wrote:
> I am doing some research on CPU intensive computer simulation
> techniques, more specifically monte carlo simulations and analysis.
> Basically I'm trying to get a feel for real world usage models,
> methodologies, tools, techniques, and general experiences. Any and all
> feedback would be greatly appreciated.

Not, that I'm an expert, rather also just starting to work with MC, but 
maybe it helps.

> What tools do you use to perform simulations, and more specifically
> Monte Carlo type simulations? I assume those reading this newsgroup are
> using Mathematica, but how specifically are you using it? What other
> tools do you / have you used statistical math packages, spreadsheet
> plug-ins, homegrown code, other?

The code that actually simulates the system I have written in C++, from 
scratch. I thought that the core of the whole thing should be fast, and 
so C++ with STL seemed a reasonable choice for me.

Occasionally, there is an equation system over the Boolean field GF(2) 
to be solved, and for this, the C++ code asks Mathematica, via MathLink. 
That works quite nice.

> How long do your simulations typically take to complete?

Typically, is takes between half an hour to one week-end for enough 
statistics to have accumulated so that the result is useful.

> What techniques, if any, do you use to reduce your simulation time?

Optimizing the core of the simulator. Making sure, all algorithms in 
inner loops are fast. Importance sampling.

The latter stays at a basic level, as all those sophisticated Markov 
Chain MC ideas don't seem to apply. But it can make a huge difference.

> What class of computer Hardware do you use?
> (PC, supercomputer, low cost HPC cluster, other?)

I test everything on my desk PC, and then do actual performance on our 
university's cluster, which offers ca. 20 nodes, each with Dual Xeon 
processors. But I don't use all nodes in oder not to annoy my collegues. ;-)

> What kind of applications (generally) are you applying Monte Carlo
> analysis to?

Well, quantum gate networks in my case. But that is surely not a typical 
application.

> I have access to general information on Monte Carlo Simulation, but I'm
> more interested in real world uses and users. Any links to that type of
> information, discussion groups, etc... again would be greatly
> appreciated.

A discussion group about MC would be quite nice indeed. So, unless 
somebody points us to one, I would suggest to just start one, either by 
newsgroup or by mailing list.

A first start might be, however, sci.math.num-analysis.

HTH
   Simon