## Uncertainty Quantification

### Overview

__Overview__

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.

This group contains the following:

__Introduction to Uncertainty Quantification__

### Short Course: Introduction to Uncertainty Quantification

Taught by Alejandro Strachan, Purdue University.

The objective of this summer school on Uncertainty Quantification and its Applications is to present an accessible introduction to the basic tools of uncertainty quantification, with the goal of orienting attendees to the field and helping them address UQ questions in their application areas of interest. Lectures will provide basic introductions to probability and stochastic processes, data analysis, estimation and inference, sensitivity analysis, uncertainty propagation, sampling methods, Bayesian computation, experimental design, and model validation. In addition, several guest lecturers will present a diverse set of applications and snapshots of current research, in which uncertainty quantification plays an important role.

### A Gentle Introduction to Uncertainty Quantification

Professor Ilias Bilionis, Purdue University

### How to add UQ to Rappture Tools

Uncertainty Quantification (UQ) is a new feature in Rappture.

This presentation discusses: What is it? Why would you need it? How does it work? How do you use it?

__Graduate Courses__

**Introduction to Uncertainty Quantification**

**ME597/AAE590 at Purdue University (2010) ** 3 Lectures.

Taught by Alina Alexeenko

Selected Topics: uncertainty quantification, propagation, molecular dynamics simulations

**Characterization, Material/Process Dependence and Predictive Modeling**

**Indian Institute of Technology Bombay (2012). ** 3 Lectures.

Taught by Souvik Mahapatra

Selected Topics: CMOS, CMOS device reliability, device characterization, device modeling, MOSFET, MOSFET modeling, nanoelectronics, negative bias temperature instability, reliability