Model perfect

February 22, 2016

Mathematical models are used to predict just about everything from traffic and weather to plant metabolism and industrial biotechnology.

However, while they are valuable tools in a broad range of fields, predictive models are still plagued by uncertainties, or errors, and a great deal of effort is directed at determining the extent and effects of these errors.

Now, a team of researchers led by the University of Delaware's Dion Vlachos has developed a framework to address this issue by looking at the effects of correlated parameters.

Their work appears in a paper published in Nature Chemistry on Monday, Feb. 22.

Vlachos explains that all mathematical models comprise a number of measures, known as parameters. Weather forecast models, for example, include dozens of parameters from temperature and precipitation to wind speed and lightning.

Slight errors in any one of these measures can cause model predictions to veer off course -- which is why meteorologists are not sure whether an approaching storm will become a blizzard in the Mid-Atlantic region or swing out to sea just north of the Carolinas and leave kids in Delaware disappointed that they didn't get a snow day.

In evaluating the effects of such errors, researchers have traditionally assessed each of them separately and then "added them up," which, as it turns out, can lead to overestimation.

Vlachos uses a simple analogy to explain why.

"If you and a friend each have four reasons for wanting to live in the city, that might sound like a total of eight reasons," he says. "But if three of your reasons overlap, the list ends up with only five items, not eight."

"It's the same with model parameters," he continues. "When we looked at correlations among parameters and their dependence on each other, we realized that the errors were not nearly as large as we thought they were."

The paper documents the team's work on predicting the collective behavior of reaction networks, with the goal of improving chemical transformations in catalysis.

However, the approach has applications in fields ranging from catalysis and combustion to environmental sciences and biology.

"Models are more robust and reliable than we thought they were," says Vlachos. "It makes sense that the parameters are interdependent and that you can't change one without affecting the others, whether you're talking about global warming or wastewater treatment."
About the research team

The paper, "Effects of Correlated Parameters and Uncertainty in Electronic-Structure-Based Chemical Kinetic Modeling," was coauthored by Jonathan E. Sutton, Wei Guo, Markos A. Katsoulakis, and Dionisios G. Vlachos

Sutton, who earned his doctoral degree at UD in 2014, is now a postdoctoral research associate at Oak Ridge National Laboratory.

Guo is a visiting scholar at UD's Catalysis Center for Energy Innovation.

Katsoulakis is a professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

Vlachos is Elizabeth Inez Kelley Professor of Chemical and Biomolecular Engineering and director of the Catalysis Center for Energy Innovation.

University of Delaware

Related Mathematical Models Articles from Brightsurf:

A new mathematical front to understand species coexistence
In an effort to understand how different species coexist, researchers develop a mathematical model that establishes interactions in co-colonization as the key.

How genetic variation gives rise to differences in mathematical ability
DNA variation in a gene called ROBO1 is associated with early anatomical differences in a brain region that plays a key role in quantity representation, potentially explaining how genetic variability might shape mathematical performance in children, according to a study published October 22nd in the open-access journal PLOS Biology by Michael Skeide of the Max Planck Institute for Human Cognitive and Brain Sciences, and colleagues.

Mathematical modelling to prevent fistulas
It is better to invest in measures that make it easier for women to visit a doctor during pregnancy than measures to repair birth injuries.

New mathematical tool can select the best sensors for the job
In the 2019 Boeing 737 Max crash, the recovered black box from the aftermath hinted that a failed pressure sensor may have caused the ill-fated aircraft to nose dive.

The mathematical values of Linear A fraction signs
A recent study by a team based at the University of Bologna, published in the Journal of Archaeological Science, has shed new light on the Minoan system of fractions, one of the outstanding enigmas tied to the ancient writing of numbers.

The mathematical magic of bending grids
A mathematical discovery opens up new possibilities for architecture and design: For any desired curved surface a flat grid of straight bars can be calculated that can be folded out to the desired curved structure.

An ant-inspired approach to mathematical sampling
In a paper published by the Royal Society, a team of Bristol researchers observed the exploratory behaviour of ants to inform the development of a more efficient mathematical sampling technique.

New mathematical model can more effectively track epidemics
As COVID-19 spreads worldwide, leaders are relying on mathematical models to make public health and economic decisions.

Mathematical model could lead to better treatment for diabetes
MIT researchers have developed a mathematical model that can predict the behavior of glucose-responsive insulin in humans and in rodents.

New mathematical model for amyloid formation
Scientists report on a mathematical model for the formation of amyloid fibrils.

Read More: Mathematical Models News and Mathematical Models Current Events is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to