## Uncertainty Quantification

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### Overview

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## Welcome to the Uncertainty Quantification group!

The integration of the PRISM Uncertainty Quantification (PUQ) software into nanoHUB and the Rappture toolkit provides nanoHUB users with powerful tools for uncertainty propagation, statistical model calibration and data analysis, and validation of simulations that will eventually enable predictions with quantified confidence. Users can now propagate uncertainties in inputs and quantify how they affect outputs. The beauty of this integration is that UQ is automatically available to the vast majority of nanoHUB tools (those built using the Rappture toolkit) without changing the underlying deterministic code: all the tasks involved are performed automatically by the cyberinfrastructure.

The overall approach for uncertainty propagation in nanoHUB is based on the method of collocation followed by the the construction of surrogate models (also called response surfaces) through which input distributions can be propagated in a computationally efficient manner.

As shown in the figure, users can easily specify input variables in terms of distributions by clicking on the distribution button that is automatically added to all real-valued inputs. Given the specified distributions of input parameters and the number of simulations the user is willing to perform, PUQ selects optimal collocation points using Smolyak sparse grids. Using the Rappture submit command the deterministic code underlying the tool is executed for each set of the collocation points.

Once the simulations finish, the results are then used to construct Reduced Order Models (ROM) using generalized polynomial chaos and to compute the sensitivity of each output to the uncertain inputs, see bottom-right panel in the figure. Finally the ROM is used to propagate the distributions of input parameters and predict a distribution of outputs using Monte Carlo techniques.

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