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Improving Mathematical Models with Uncertainty

Category: Science & Technology
Posted: 05:34AM
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In science classes the concept of 'ideal conditions' can often be invoked, because under ideal conditions, complex systems can be made simpler. Outside of classes complex systems are still simplified by removing complicating terms, but such a sacrifice can also make a mathematical model inaccurate. Researchers at Brown University are working to repair these inaccuracies by adding uncertainty to the models for some very complex systems.

Predicting the weather is not easy, evidenced by the number of times a forecast is wrong, and part of the process for doing that is modelling how pressure waves interact, which we do have equations for. While those generalized equations do successfully model the interactions, they fail to consider other variables that also impact the waves, such as the geography beneath them, for the sake of simplicity. The Brown researchers are trying to correct that by adding a random term to the model as a random forcing. This will result in the model producing a range of values, instead of a single answer, and will make it more realistic.

This work is part of a mathematical field called uncertainty quantifications, which tries to recover some degrees of freedom removed by simplification, as a random forcing. The reason this is only being done now is that computing power has only recently reached the level needed for this work.

Source: Brown University



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