Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin

Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Recent Advances in Dakota UQ

Patricia D. Hough Quantitative Modeling and Analysis

Brian M. Adams Optimization and Uncertainty Quantification

http://dakota.sandia.gov 2016 SIAM Conference on Uncertainty Quantification April 5—8, 2016 Lausanne, Switzerland

SAND2016-3016C

DAKOTA GOALS AND CAPABILITIES

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SNL Mission: Advanced Science and Engineering for National Security

Nuclear Weapons

Defense Systems and Assessments

Energy and Climate

International, Homeland, and Nuclear Security

Strong research foundations span many disciplines

Dakota Mission: To serve Sandia’s mission through state-of-the-art research and robust, usable software for optimization and uncertainty quantification.

Dakota Team: has balanced strengths in algorithm research, software design and development, and application deployment and support

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Dakota: Algorithms for Design Exploration and Uncertainty Quantification

Suite of iterative mathematical and statistical methods that interface to computational models

Makes sophisticated parametric exploration of black-box simulations practical for a computational design-analyze-test cycle:

Sensitivity Analysis

Uncertainty Quantification

Design Optimization

Model Calibration

Goal: provide scientists and engineers (analysts, designers, decision makers) richer perspective on model predictions

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simulation

model

input

parameters

response

QOIs

Diverse Simulations Across Scales

Emergencies: weather,

logistics, economics, human

behavior Electrical circuits: networks,

PDEs, differential algebraic

equations (DAEs), E&M

Shock loading of polymer

foam: molecular dynamics

Micro-electro-mechanical

systems (MEMS): quasi-static

nonlinear elasticity, process

modeling

Joint mechanics: system-level

FEA for component

assessment

Systems of systems

analysis: multi-scale,

multi-phenomenon

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Supports Overall Simulation Workflow Including Verification and Validation

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Enables quantification of margins and uncertainty (QMU) and design with simulations; analogous to experiment-based QMU and physical design/test…

uncertainty-aware validation

verification

calibration / comparison

with data

design of computer

experiments

sensitivity analysis to

down-select

ASME Guide for V&V in Computational

Solid Mechanics

Many Methods in One Tool

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Sensitivity Analysis • Designs: MC/LHS, DACE, sparse

grid, one-at-a-time • Analysis: correlations, scatter,

Morris effects, Sobol indices

Uncertainty Quantification • MC/LHS/Adaptive sampling • Local/global reliability • Stochastic expansions • Epistemic methods • Multi-fidelity/multi-level

Optimization • Gradient-based local • Derivative-free local • Global/heuristics • Surrogate-based, multi-fidelity

Calibration • Tailored gradient-based • Use any optimizer • Bayesian inference

One flexible simulation interface, many methods: once interface created, apply appropriate algorithm depending on question at hand

Scalable parallel computing from desktop to HPC

Engineering Needs Drive Dakota R&D

Advanced approaches help you solve practical problems, including with non-smooth, discontinuous, or multi-modal responses:

Characterize parameter uncertainty → Bayesian calibration

Hybrid analysis → mix methods, surrogates, and models

Mixed uncertainty characterizations → epistemic and mixed uncertainty forms and propagation

Costly simulations → surrogate-based, multi-fidelity optimization and UQ

Build in safety or robustness → combined deterministic/ probabilistic methods

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min

s.t.

Dakota History and Resources

Genesis: 1994 optimization LDRD

Modern software quality and development practices

Released every May 15 and Nov 15

Established support process for SNL, partners, and beyond

Extensive website: documentation, training materials, downloads

Open source facilitates external collaboration; widely downloaded

Mike Eldred,

Founder

Lab mission-driven algorithm R&D deployed in production software

http://dakota.sandia.gov

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RECENT AND FUTURE DAKOTA DEVELOPMENT

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MLE

MAP

Inference: Bayesian Calibration

Goal: Obtain statistical characterization of parameters consistent with data

MCMC with DRAM and DREAM; emerging non-MCMC-based approaches

Research (Eldred) in adaptive, surrogate-based inference; use derivatives to precondition proposal covariance to increase acceptance rates

Usability: support all variable types, chain post- processing, statistics, credible/prediction intervals, KDE-smoothed posteriors, mutual information

Experiment data and covariance handling

Next: model discrepancy, iterative DOE

Collaborations: UT Austin, LANL, NC State

See also Tezaur (MS2): Bayesian calibration for land-ice models; McDougall (MS56): QUESO software

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Core UQ Method Improvements Robust, scalable, usable UQ methods

Sampling

New: Incremental and batch sampling, Wilks criterion-based sample size, D-optimal designs based on Leja sequences

Improved adaptive importance sampling

New recursive k-d darts (RKD) sampling; see Rushdi (MS114)

Generalized multi-level Monte Carlo; see Eldred (MS73) Geometric to treat multiple discretization levels (ML)

Control variate to treat multiple hierarchical model forms (MF)

Stochastic Expansions

Non-intrusive polynomial chaos, stochastic collocation, various integration schemes, adaptivity

Adaptive basis selection for compressed sensing; see Jakeman (MS57)

Import/export of expansions and approximate evaluations

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D-optimal design for

discrete variables

Active Subspace Identification

Goal: Scale sensitivity analysis, UQ, optimization, and surrogates by finding an input parameter subspace

Many algorithm, correctness, and usability improvements (Monschke)

Several subspace identification criteria

Can perform UQ with sampling, PCE, and reliability methods; others and more variables types coming

Next: derivative-free approaches (with NC State)

See also Constantine (MS46, PP101)

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𝑥 = 𝑾𝟏𝑦 + 𝑾𝟐𝑧

Constantine, 2015

Piecewise Local Surrogates Build on meshing research: maximum Poisson disk sampling,

approximate Voronoi cell identification, recursive k-d darts

Construct global (piecewise local) surrogates with discontinuity detection, without explicit meshing

See also Ebeida (MS136), Rushdi (MS114)

Random Field Modeling

Goal: perform UQ with field-valued (time- or space-varying) input uncertainties f(t, x), e.g., boundary conditions

Generate realizations of f(t; u): either sample the field-generating model or use offline data

Approximate uncertainty in f(t; u), e.g., by a Karhunen–Loève expansion with normal coefficients ω

Propagate: perform UQ over ω, generating

realizations of the approximate field 𝒇 𝑡, 𝜔 and propagate through the field-accepting model

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field-

generating

model

uncertain input

parameters u

ultimate quantities of

interest

𝒇 𝑡, 𝜔 = 𝝁𝒇 𝒕 + 𝑐𝑖 𝜔

𝑃

𝑖=1

𝜑𝑖 𝑡

field-

accepting

model

field-valued outputs

f(t,x;u) become inputs

Promote User and Development Community Engagement

Web resources: Interactive user forums

Capability maturity ratings and test linkage

Community repository of code, examples, scripts

Training materials: presentations, videos, exercises

New graphical user interface for Dakota analysis

Improved modularity so users can extend, contribute components, e.g., Surrogate model module with Python bindings

More usable simulation interfacing that encourages best practices

Communicate development practices to encourage contribution, e.g., principles, code standards, easier build/test on new platforms

Portability to and scalability on new high-performance computers

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Engaging Dakota Algorithms for Design Exploration and Uncertainty Quantification

Website: http://dakota.sandia.gov Download (LGPL license, freely available worldwide)

Getting Started guide

User’s Manual, Chapter 2: Tutorial with example input files

Extensive documentation (user, reference, developer)

Support mailing list (reaches both Dakota team and user community)

At SIAM UQ 2016 Talk to: Eldred, Hough, Jakeman, Stephens, Stewart; Ebeida, Maupin, Rushdi

See poster: Dakota applied to a V&V challenge problem (Stephens/Hough; PP102)

Thanks for your attention! pdhough@sandia.gov briadam@sandia.gov

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