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Quantification of Uncertainty in Extreme Scale Computations

Debusschere, Bert D.; Jakeman, John D.; Chowdhary, Kamaljit S.; Safta, Cosmin S.; Sargsyan, Khachik S.; Rai, P.R.; Ghanem, R.G.; Knio, O.K.; La Maitre, O.L.; Winokur, J.W.; Li, G.L.; Ghattas, O.G.; Moser, R.M.; Simmons, C.S.; Alexanderian, A.A.; Gattiker, J.G.; Higdon, D.H.; Lawrence, E.L.; Bhat, S.B.; Marzouk, Y.M.; Bigoni, D.B.; Cui, T.C.; Parno, M.P.

Abstract not provided.

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TYPE Conference Poster YEAR 2015
OSTI

CSPlib - A Software Toolkit for the Analysis of Dynamical Systems and Chemical Kinetic Models

Diaz-Ibarra, Oscar H.; Kim, Kyungjoo K.; Safta, Cosmin S.; Najm, H.N.

CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.

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TYPE SAND Report YEAR 2021
OSTIDOI

Global sensitivity analysis and estimation of model error, toward uncertainty quantification in scramjet computations

AIAA Journal

Huan, Xun H.; Safta, Cosmin S.; Geraci, Gianluca G.; Eldred, Michael S.; Vane, Zachary P.; Lacaze, Guilhem M.; Oefelein, Joseph C.; Najm, H.N.

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertainparameters involvedandthe high computational costofflow simulations. These difficulties are addressedin this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying themin the current studyto large-eddy simulations ofajet incrossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system's stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. These methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

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TYPE Journal Article YEAR 2018
ScopusOSTIDOI

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

AIAA Journal

Huan, Xun H.; Safta, Cosmin S.; Sargsyan, Khachik S.; Geraci, Gianluca G.; Eldred, Michael S.; Vane, Zachary P.; Lacaze, Guilhem L.; Oefelein, Joseph C.; Najm, H.N.

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. Finally, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

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TYPE Journal Article YEAR 2018
OSTIDOI

Greenhouse Gas Source Attribution: Measurements Modeling and Uncertainty Quantification

Liu, Zhen L.; Safta, Cosmin S.; Sargsyan, Khachik S.; Najm, H.N.; van Bloemen Waanders, Bart G.; LaFranchi, Brian L.; Ivey, Mark D.; Schrader, Paul E.; Michelsen, Hope A.; Bambha, Ray B.

In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO2 . This will allow for the examination of regional-scale transport and distribution of CO2 along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developed a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO2 inversions. We have tested the approach using data and model outputs from the TransCom3 global CO2 inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO2 , CH4 and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.

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TYPE SAND Report YEAR 2014
OSTIDOI

Interatomic Potentials Models for Cu-Ni and Cu-Zr Alloys

Safta, Cosmin S.; Geraci, Gianluca G.; Eldred, Michael S.; Najm, H.N.; Riegner, David R.; Windl, Wolfgang W.

This study explores a Bayesian calibration framework for the RAMPAGE alloy potential model for Cu-Ni and Cu-Zr systems, respectively. In RAMPAGE potentials, it is proposed that once calibrated potentials for individual elements are available, the inter-species interac- tions can be described by fitting a Morse potential for pair interactions with three parameters, while densities for the embedding function can be scaled by two parameters from the elemen- tal densities. Global sensitivity analysis tools were employed to understand the impact each parameter has on the MD simulation results. A transitional Markov Chain Monte Carlo al- gorithm was used to generate samples from the multimodal posterior distribution consistent with the discrepancy between MD simulation results and DFT data. For the Cu-Ni system the posterior predictive tests indicate that the fitted interatomic potential model agrees well with the DFT data, justifying the basic RAMPAGE assumtions. For the Cu-Zr system, where the phase diagram suggests more complicated atomic interactions than in the case of Cu-Ni, the RAMPAGE potential captured only a subset of the DFT data. The resulting posterior distri- bution for the 5 model parameters exhibited several modes, with each mode corresponding to specific simulation data and a suboptimal agreement with the DFT results.

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TYPE SAND Report YEAR 2018
OSTIDOI

Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

Safta, Cosmin S.; Najm, H.N.; Phipps, Eric T.

Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.

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TYPE SAND Report YEAR 2014
OSTIDOI

Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem

Journal of Aerospace Information Systems

Safta, Cosmin S.; Sargsyan, Khachik S.; Najm, H.N.; Chowdhary, Kenny; Debusschere, Bert D.; Swiler, Laura P.; Eldred, Michael S.

In this paper, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory-epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.

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TYPE Journal Article YEAR 2015
ScopusOSTIDOI

Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning

Journal of Machine Learning Research

Gorodetsky, Alex A.; Safta, Cosmin S.; Jakeman, John D.

This paper describes an efficient reverse-mode differentiation algorithm for contraction operations for arbitrary and unconventional tensor network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have a single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve eficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.

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TYPE Journal Article YEAR 2022
ScopusOSTI
Results 1–50 of 60
Results 1–50 of 60