MADNESS calms chemistry on computers
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The mathematical methods Beylkin, Fann, and Harrison created can compute structures in multiple dimensions – Beylkin has run model calculations on as many as 30 – faster and more precisely. That can help scientists simulate or predict experiments, letting them focus on the most promising areas.
Chemistry and materials science were good matches to test their methods, Fann says. They’re “rich in high-dimensional problems and they want very high precision,” he adds. “The scientists write the equations, and we’re writing the math for solving those equations.”
That math relies on approximating both mathematical expressions and the operations performed on them through a sequence of spatial scales. “It actually allows us to finely resolve points of interest through increasing details,” Fann says. “The difference is that we actually compute at one level, but for subsequent levels we keep track of the differences, so we only add in the additional information or improvements to the resolution.”
The ability to compute at different levels of detail means researchers can choose to focus their simulations on areas that interest them most. This multiresolution approach – using coarse-scale models that adapt to capture fine-scale detail – also uses computer power more efficiently.
Fann compares it to looking at a picture. You can see the whole image, but if something important catches your eye, you’ll focus on that. As you examine it more closely, your eyes gloss over the rest of the image.
Picking the precision
The MADNESS algorithms also let researchers choose how precise they want the calculations to be. “We go to the level of detail necessary to get the precision,” Fann says. That’s especially important in molecular chemistry, when scientists compare energy levels – the arrangement of electrons in atoms, molecules and other structures. The differences can be very fine, requiring as much as 12 decimals of accuracy, Fann says.
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