Uncertainty Quantification Area

FASTMath UQ Team

1Sandia National Laboratories, Livermore, CA

2Sandia National Laboratories, Albuquerque, NM

3University of Southern California, Los Angeles, CA

4Massachusetts Institute of Technology, Cambridge, MA

FASTMath All-Hands MeetingArgonne National Lab.

June 10-11, 2019

Overview

UQ work under FASTMath includes

Enhancing deployed UQ capabilities in Dakota & UQTkCoupling with MIT UQ library (MUQ)

Low rank tensor methods for dealing with high-D functionsManifold learningAdaptive basisBayesian inferenceUQ with model errorInference in dynamical systemsMultilevel Multifidelity methodsOptimization under uncertainty

ASCR base funding on networks, stochastic dynamical systems,probabilistic computing, etc has contributed to the development andhardening of our UQ software over a number of years

SNL Najm Comp 2 / 14

FASTMath UQ Team

Sandia – CA

Habib NajmBert DebusschereCosmin SaftaKhachik SargsyanTiernan Casey

MIT

Youssef Marzouk

Sandia – NM

Michael EldredJohn JakemanGianluca Geraci

USC

Roger Ghanem

SNL Najm Comp 3 / 14

Partnerships – 1

Plasma Surface Interactions: Predicting the Performance and Impact ofDynamic PFC Surfaces (PSI2) [SC-FES]

Modeling transport of He gas bubbles in ITER divertor materialBayesian estimation, global sensitivity analysis (GSA), forward UQ

Simulation of Fission Gas in Uranium Oxide Nuclear Fuel [NE]

Modeling noble gas bubble transport in nuclear fuel rod materialBayesian estimation, GSA, forward UQ

Optimization of Sensor Networks for Improving Climate ModelPredictions (OSCM) [SC-BER]

Energy Exascale Earth System Model (E3SM) Land ComponentForward UQ and GSA: high-dimensionality challengesBayesian estimation of model parameters with model structural errorOptimal experimental design for measurement sensor placement

SNL Najm Comp 4 / 14

Partnerships – 2

Probabilistic Sea Level Projections from Ice Sheet and Earth SystemModel (ProSPect) [SC-BER]

Goal: Estimate uncertainty in predictions of sea-level rise due toice-sheet evolutionHigh-dimensionality (Hi-D) challenges of forward UQHi-D challenges of Bayesian inference of model parametersMoving toward using multi-fidelity algorithms for above tasks

SNL Najm Comp 5 / 14

High Dimensional Function Approximation-Dependence

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Efficiently building surrogates of models parameterized by dependentrandom variables is challenging:

Probabilistic transformations introduce non-linearitiesApproaches not accounting for PDF of variables are inefficient

Solution:

Generate orthonormal polynomial basis and weighted Leja sequenceTarget accuracy in high-probability regions while maintaining stability

John D. Jakeman, Fabian Franzelin, Akil Narayan, Michael Eldred, Dirk Pflüger, “Polynomial chaos expansions for dependent random variables”,Computer Methods in Applied Mechanics and Engineering, Volume 351,2019, Pages 643-666, https://doi.org/10.1016/j.cma.2019.03.049.

SNL Najm Comp 6 / 14

High Dimensional Function Approximation - Low Rank

E3SM Simulation

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Tensor-train Schematic

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Seek low-rank functional tensor-train representation to reveal couplings inhigh-dimensional models.

Compressed representation, can result in a sample complexity which isonly weakly dependent on dimensionCan combine local/global approximations in a compact model

Next Steps:

Embed parametric dependencies into a generalized low-rankfunctional tensor-train decompositionAdaptive sampling of mixed stochastic/physical spaces to targetregions of high-probability/non-linear behavior in the joint space

SNL Najm Comp 7 / 14

UQTk Developments

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Convergence study of adapted PC for 600−dimensionalcrash analysis problem with hardening plasticity

RF order 3 dim=2RF order 3 dim=2RF order 3 dim=3RF order 3 dim=4RF order 3 dim=5RF order 3 dim=6

In-progress integration of new capabilitiesCoupling between UQTk and MUQ – C++/PythonBasis adaptation with error correctionManifold learning and sampling

Improved User experienceBug fixes, more documentation, better user interfacesNew tutorials – e.g. Bayesian model selection

Version 3.1.0 this summer — push to github for easier distribution

SNL Najm Comp 8 / 14

Dakota highlights

Dakota version 6.10 released May 15, 2019Hardening of multilevel-mutifidelity surrogate approachesAdaptivity through greedy multilevel refinement

Prototyped integration with Legion AMT for ensemble UQ workflowswith Stanford

Exploited special structure w/functional tensor train approximationIntegrated Compressed Continuous Computation (C3) package– from Alex Gorodetsky, U. MichiganMultidimensional functions represented in low-rank format– sample requirements scale linearly w/dimension 𝑂(𝑑𝑟2)

In progressIntegration of MUQ library (w/ MIT and CRREL)Integration of Adaptive Basis for dimension reduction (w/ USC)

SNL Najm Comp 9 / 14

MLMF/OUU Algorithmic highlights

Advancements on multifidelity/multilevel approaches for UQ

Surrogate-based approachesMultilevel expansions

Polynomial chaos, projection, regression, stoch. collocationFunctional tensor train (in progress)

Adaptive refinementIsotropic, anisotropic, index set, expanding front

Sampling-based approaches (more in the poster)A Generalized Framework for Approximate Control Variates

(arXiv: 1811.04988v3)

Optimization Under Uncertainty (OUU)

Verification cases to test SNOWPAC + MC-based UQ with error est.Fall 2019: multifidelity global opt. with GPs (MF EGO)2020: multifidelity OUU for Tokamaks (TDS)

SNL Najm Comp 10 / 14

Advances in Bayesian Methods

Systematic framework for embedded model error quantificationAllows predictive uncertainty attribution into components due to modelsurrogate construction, data noise and model errorWorkflow is implemented in UQTk and is employed in DOE and DODprojects, including turbulence modeling, fusion science and land model

(K. Sargsyan, X. Huan, HNN; Int. J UQ 2019)

MCMC acceleration via local surrogatesNew rate-optimal refinement strategies balance surrogate and sampling error

(Davis, Smith, Pillai, Marzouk 2019)

Explicit control of Lyapunov function guarantees convergence forheavier-tailed distributions, broadens robustness and applicability

Distance metrics for likelihood construction for dynamical systems

Comparison of chaotic dynamicaltrajectories using distances betweendensities defined in manifold coordinates

Global diffusion-map distance forconstructing Bayesian likelihoods inparameter estimation

SNL Najm Comp 11 / 14

Non-SciDAC Engagement – 1

SECURE: An Evidence-Based Approach for CybersecurityC. Safta, J. Jakeman, G. Geraci, B. Debusschere – [SNL Grand Chall. LDRD]

Adaptive sampling for quadrature on discrete random variables– developed and applied to SECURE relevant models

Analysis of redox potentials in H2 advanced water splitting materialsB. Debusschere – [DOE EERE]

Application of UQTk for model comparison and model errorcomputation to water splitting reactions for Hydrogen production.Work led to tutorials that have in turn been incorporated in UQTk

Bayesian Optimal Experimental DesignH. Najm – [DOE BES]

Application of UQTk surrogate construction and Bayesian capabilitiesOptimal design of a mass spectrometry expt at the ALS

SNL Najm Comp 12 / 14

Non-SciDAC Engagement – 2

Partnering w/U. Michigan - flood modeling – K. Sargsyan – [NSF]

Surrogate construction, sensitivity analysis and parameter estimationfor the ecohydrologic model using data observed in Manaus, Brazil

M. C. Dwelle, J. Kim,K. Sargsyan, V. Ivanov, “Streamflow, stomata, and soil pits: sources of inference for complex models with fast, robustuncertainty quantification”, Advances in Water Resources, Volume 125, pp. 13-31, March, 2019

Energy Exascale Earth System Model (E3SM) – K. Sargsyan – [SC-BER]

UQTk is employed for sensitivity analysis and model calibrationD. Ricciuto, K. Sargsyan, P. Thornton, The Impact of Parametric Uncertainties on Biogeochemistry in the E3SM Land Model, Journal of Advances inModeling Earth Systems, Vol. 10, No. 2, p.297–319, 2018

Atmosphere to electrons (A2e) – M. Eldred, G. Geraci – [EERE]

Dakota and multilevel / multifidelity algorithms deployed forforward / inverse UQ and OUU in wind plant applications

SNL Najm Comp 13 / 14

Non-SciDAC Engagement – 3 – R. Ghanem

Risk assessment for spent fuel containment structures – [NNSA]

UQ analysis of a high-fidelity model of a fuel cask systemUQ models to characterize damage following transport

Hazard maps for tsunami storm surge – [NSF]

Assessment of topography effect on run-up during a tsunami event

Modeling and design of a lightweight composite car – [DOE]

Adaptive basis in very high-dimensional coupled physics problems.

Probabilistic machine learning (PML) for physics discovery – [DARPA]

Integration of manifold sampling with genetic programming to carrysymbolic regression for candidate mathematical models.Adaptation of PML to large scale OUU; scramjet design optimization

SNL Najm Comp 14 / 14