Error estimation improves multiscale models

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Multiscale is multidisciplinary

The Department of Energy’s Office of Advanced Scientific Computing Research is supporting Oden’s work to refine algorithms – mathematical recipes computers use – that represent physical processes at multiple scales.  Oden works with a team of mathematicians, chemists, chemical engineers and others to incorporate error estimation into mathematical models, then adapt the models to minimize that error.

The process, called adaptive modeling, is based on what Oden called a revelation: That techniques used to estimate error in models at the scale of atoms or molecules can apply to larger scales, too.

The researchers start with a base model – a mathematical model of a system at the atomistic or molecular level.  The nature and number of elements at this minuscule level make the model “so complex and intractable that you don’t have a hope of solving it.  You don’t want to solve it,” Oden says, but the base model is a way to judge other, coarser models set at larger scales.  Unlike the base, these “surrogate” models can be solved, Oden says.

“The beautiful thing is when we solve it we can estimate the error,” he adds.  “If we’re not happy with the error, we need a technique to refine the surrogate and make it more sophisticated.”

That’s the other part of Oden’s research: Goal-oriented error estimation.  When researchers run computer models of physical systems, they typically choose just a few things they want to know about most.  Oden’s group wants to focus error estimation on those areas so researchers can judge the reliability of the results.

“To be able to estimate the error puts the analyst in an extremely strong position,” Oden says.  Researchers can determine if the model violated any important principles.  They can decide whether the error level is acceptable, or if the problem should be examined at a different scale for a more precise answer.

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