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The so-called ‘Monte Carlo’ method is widely used for computer modelling in science, engineering and industry. Named after a famous casino in Monaco, it relies on random numbers to simulate events and the motion of particles in the real world.
For the results to be reliable, the numbers used must be truly random, which is not possible with computer-generated numbers. At best, they are ‘pseudo-random’, depending in a complicated way on initial conditions but usually indistinguishable from genuinely random numbers. Or so everyone thought.
‘The generators introduced in recent decades had some weak properties which influenced the results, and they were less suitable for demanding Monte Carlo simulations,’ says George Savvidy of the Demokritos National Center for Scientific Research in Athens and coordinator of the EU-funded MIXMAX project. ‘So we have developed and implemented a new generation of state-of-the-art random number generators.’
Maximum chaos
In 1986, Savvidy realised that the random number generators used in particle physics simulations were not as reliable as believed. Together with his wife, Natalia, he proposed a new approach based on chaos theory, exploiting a class of mathematical objects known as maximally chaotic Kolmogorov-Anosov systems.
Savvidy knew that for the new method to be practical he had to create a computer program to produce high-quality numbers at very high speed. ‘For research, you need to generate billions and billions of numbers,’ he says. ‘A good generator should be maximally chaotic and generate numbers in nanoseconds.’
A breakthrough came in 2015 when Savvidy’s son, Konstantin, published an algorithm for the new method, now known as MIXMAX, which slashed the computing time for generating random numbers. The four-year project then set out to develop a robust implementation.
‘MIXMAX is now one of the fastest generators on the market able to produce genuine 64-bit random numbers in a few nanoseconds,’ says George Savvidy.
Partners in the project have already put MIXMAX through its paces. It has been implemented in toolkits for data processing and simulations at CERN and is being used to design experiments at the Large Hadron Collider. It is assisting research into quantum gravity at the Niels Bohr Institute in Copenhagen and into fundamental particle physics at the Yerevan Physics Institute in Armenia.
Lower energy bills
The potential impact is huge. Outside physics, Monte Carlo simulations are used in molecular chemistry, materials science, computational biology, computational pharmacology and computational and statistical genetics. Applications range from the design of shielding for protecting satellites from cosmic rays to calculations of the correct dose for proton-beam radiotherapy.
Although the software is open source and freely available, Savvidy is planning to set up a company to market a commercial version of MIXMAX. He sees a demand in the many supercomputing centres that run simulations for applications such as weather forecasting.
‘Advanced Monte Carlo simulations usually take many months of computer time,’ he says. ‘The highly efficient MIXMAX generator reduces the simulation time and the consumption of energy which makes computations more environmentally friendly.’
Savvidy estimates that the world’s top 500 supercomputer centres consume at least 8 million megawatt-hours of electrical energy each year at a cost of USD 1 billion. ‘About 2-3 % of the computer power is used for the generation of the random numbers for Monte Carlo simulations,’ he points out. ‘The MIXMAX software can reduce this by 30-40 % resulting in millions of dollars of savings annually.’
The MIXMAX project was funded by the EU’s Marie Skłodowska-Curie programme to promote exchange of researchers between the partner organisations.