Uncertainty Quantification Reintroduces Degrees of Freedom

Mathematicians at Brown University have introduced a new element of uncertainty into Burgers' equation, which is used to describe turbulence and shocks in fluid flows.

George Karniadakis, Heyrim Cho, and Daniele Venturi have added a new term to Burgers' equation, one that produces a range of solutions accounting for uncertain external conditions that could be acting on the model system. 

The work is part of a growing field called uncertainty quantification (UQ). Karniadakis explains:

The general idea in UQ is that when we model a system, we have to simplify it. When we simplify it, we throw out important degrees of freedom. So in UQ, we account for the fact that we committed a crime with our simplification and we try to reintroduce some of those degrees of freedom as a random forcing. It allows us to get more realism from our simulations and our predictions.

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