recent advances in dakota uqneckel/siamuq16_slides_minisymp/2016... · design-analyze-test cycle:...
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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
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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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! [email protected] [email protected]
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