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# ESP Via Mathematics in Uncertainty Quantification

## Researchers at Pacific Northwest National Lab are turning ambiguity into accuracy.

Fortune tellers use a crystal ball to make predictions, but when it comes to reducing the uncertainty and making better prediction in scientific data, researchers want something a little more accurate.

Current processes for uncertainty quantification (UQ) of large-scale complex systems, such as using climate models for predicting global warming scenarios are "computationally expensive," meaning it takes a long time to run the necessary simulations, especially since multiple large-scale simulation runs with different parameters are typically needed in uncertainty quantification. Now, researchers at PNNL and their collaborators at Cornell University have developed an efficient, Bayesian UQ framework that dramatically increases the UQ accuracy and reduces the required number of simulation runs.

The research, highlighted in the upcoming *Journal of Computational Physics* paper "Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification," outlines an efficient UQ algorithm for improving predictive capabilities of large-scale complex systems in a wide range of applications. The new method can provide analytical point estimates, as well as error bars, for the statistics of interest. Numerical tests demonstrate the effectiveness of the new method in identifying discontinuities, local features and adaptively performing simulation runs only at the location with largest uncertainty.

One possible UQ application example using the newly-developed method is prediction of the plume migration of supercritical carbon dioxide in subsurface modeling for carbon sequestration. To obtain the information on the rock property at various locations, localized measurements can be taken, but that doesn't provide enough information about the rock property in the whole area where we store the supercritical carbon dioxide. Therefore, a stochastic model – one using a wide range of random variables – is necessary to represent the spatial variation of rock property within the subsurface reservoir; and the new method can dramatically reduce the required number of simulation runs with different samples of the rock property in order to arrive at an accurate prediction of the migration of carbon dioxide in subsurface.

This new process provides the ability to perform simulation-based predictions of large-scale complex systems more easily and with a significantly higher level of accuracy. It increases confidence through providing an "error bar" – the statistical range of the accuracy of the results.

"We want to make good predictions of complex systems with an error bar," says project lead Guang Lin, a computational mathematics researcher at PNNL. "This provides us confidence for critical decision-making."

In addition to climate and subsurface, the new methodology has applications in many scientific applications, including predicting the reaction rates for catalytic reactions, and predicting material properties. It can even be integrated into hurricane forecasting to improve predictability and provide more accurate estimates.

"This model is solving problems with multiple outputs observed in both time and space," says co-author Alex Konomi, also a PNNL computational mathematics researcher. "We can look at how changing the input values results in changes to the output values."

Currently existing methods are too computationally expensive to quantify the uncertainty in prediction of large-scale complex systems. This new method reduces the computationally "intense" process and enables us to be better fortune tellers in having more accurate prediction for critical decision-making.

This work was supported by the Department of Energy Office of Science Office of Advanced Scientific Computing Research.

The Department's Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information please visit http://science.energy.gov.

*MaryAnne Wuennecke is a communications specialist at Pacific Northwest National Laboratory in Richland, Wash.*