PUQ: A code for non-intrusive uncertainty propagation in computer simulations

Abstract

a b s t r a c tWe present a software package for the non-intrusive propagation of uncertainties in input parameters through computer simulation codes or mathematical models and associated analysis; we demonstrate its use to drive micromechanical simulations using a phase field approach to dislocation dynamics. The PRISM uncertainty quantification framework (PUQ) offers several methods to sample the distribution of input variables and to obtain surrogate models (or response functions) that relate the uncertain inputs with the quantities of interest (QoIs); the surrogate models are ultimately used to propagate uncertainties. PUQ requires minimal changes in the simulation code, just those required to annotate the QoI(s) for its analysis. Collocation methods include Monte Carlo, Latin Hypercube and Smolyak sparse grids and surrogate models can be obtained in terms of radial basis functions and via generalized polynomial chaos. PUQ uses the method of elementary effects for sensitivity analysis in Smolyak runs. The code is available for download and also available for cloud computing in nanoHUB. PUQ orchestrates runs of the nanoPLASTICITY tool at nanoHUB where users can propagate uncertainties in dislocation dynamics simulations using simply a web browser, without downloading or installing any software. Program summaryProgram title: PUQ Catalogue identifier: AEWP_v1_0Program summary URL: Solution method: Generalized Polynomial Chaos (gPC) using Smolyak sparse grids.Running time: PUQ performs uncertainty quantification and sensitivity analysis by running a simulation multiple times using different values for input parameters. Its run time will be the product of the run time of the chosen simulation code and the number of runs required to achieve the desired accuracy.

Uncertainty quantification of 2 models of cardiac electromechanics

“…In this work, the points in a trajectory are taken to be the same collocation points defined by the Smolyak cubature for the construction of the response surface. This reduces the computational evaluations and maximizes the spread of trajectories, so that the entire normalized parameter space is efficiently sampled . Interpretations of the sensitivity measures are in order.…”

“…The gPC method and the EEM have been implemented in the Python library PUQ, as described in Hunt et al The implementation is flexible enough to communicate with any numerical code, so we have taken advantage of this feature of PUQ to perform a forward uncertainty propagation based on the gPC method and a parameter sensitivity analysis based on the EEM using the simulations from our in‐house finite‐element code for cardiac electromechanics, which we describe next.…”

“…This reduces the computational evaluations and maximizes the spread of trajectories, so that the entire normalized parameter space is efficiently sampled. 27 Interpretations of the sensitivity measures are in order. * i determines the overall influence of parameter i on the QOI function under study.…”

Transparency in Social Media

“…nanoHUB will proactively inform users of interesting discontinuities and local optima. Further, users will be able to explore the parameter spaces studied by the community as a whole, visually identifying areas of interest that have been sparsely explored, and allowing nanoHUB to optimize the detailed study of those areas of interest through uncertainty quantification approaches (Hunt et al, 2015). nanoHUB will enable new incremental publishing mechanisms where an anchor publication about a simulation tool may be automatically augmented by groups of users employing the same tool to study different regions of parameter space as they explore nanodevices under conditions not originally conceived by the anchor publication.…”

Uncertainty Quantification of Modelling of Equiaxed Solidification

“…A low value of σ* indicates a linear dependence on the input. The algorithms and methods described in this section have been compiled into a single publically available framework along with a graphical user interface, the PRISM Uncertainty Quantification (PUQ) tool [14,15]. This tool assumes the chosen numerical model incorporates the basic physics to adequately predict the output of interest.…”