Predictive Engineering and Computational Sciences. Local Sensitivity Derivative Enhanced Monte Carlo Methods. Roy H. Stogner, Vikram Garg
|
|
|
- Brice Hancock
- 5 years ago
- Views:
Transcription
1 PECOS Predictive Engineering and Computational Sciences Local Sensitivity Derivative Enhanced Monte Carlo Methods Roy H. Stogner, Vikram Garg Institute for Computational Engineering and Sciences The University of Texas at Austin Jul 27, 2011 Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
2 Motivation and Notation Uncertainty Quantification of Large Multiphysics Problems Many uncertain, calibrated submodel parameters Computationally expensive forward evaluations Forward uncertainty propagation only of full problem Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
3 Motivation and Notation Motivation and Notation Primal/Forward Problem Parameter value(s) System solution ξ Ξ R Ξ R n ũ(x, t; ξ) U R U Primal weighted residual R(ũ(ξ), v; ξ) 0 v V Quantity of interest functional Q : U R Ξ R R Quantity of interest output q = Q(ũ(ξ), ξ) Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
4 Motivation and Notation Motivation and Notation Primal/Forward Problem Parameter value(s) System solution ξ Ξ R Ξ R n ũ(x, t; ξ) U R U Primal weighted residual R(ũ(ξ), v; ξ) 0 v V Quantity of interest functional Q : U R Ξ R R Quantity of interest output q = Q(ũ(ξ), ξ) Highly nonlinear forward solves Large finite-dimensional parameter space Few quantities of interest Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
5 Motivation and Notation Motivation and Notation Adjoint Problem Adjoint solution z(x, t; ξ) V Adjoint equation R u (ũ, z; ξ)(u) Q u (ũ; ξ)(u) u U Adjoint-based sensitivities dq dξ = Q ξ(ũ; ξ) R ξ (ũ, z; ξ) Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
6 Motivation and Notation Motivation and Notation Adjoint Problem Adjoint solution z(x, t; ξ) V Adjoint equation R u (ũ, z; ξ)(u) Q u (ũ; ξ)(u) u U Adjoint-based sensitivities dq dξ = Q ξ(ũ; ξ) R ξ (ũ, z; ξ) Linear, relatively cheap adjoint solves Free adjoints after goal-oriented refinement, error estimation Cheap quantity of interest derivatives Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
7 Motivation and Notation Motivation and Notation Uncertainty Propagation Problems Input PDF Expected (mean) output Output standard deviation ξ p ξ q E [q] Ξ q(ξ)dp R ξ σ q E [(q q) 2] Output risk P C E [q C q ] Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
8 Motivation and Notation Motivation and Notation Uncertainty Propagation Problems Input PDF Expected (mean) output Output standard deviation ξ p ξ q E [q] Ξ q(ξ)dp R ξ σ q E [(q q) 2] Output risk P C E [q C q ] Integrals in high dimensional spaces Curse of dimensionality leads us to Monte Carlo How can we enhance Monte Carlo? Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
9 Enhanced MC Latin Hypercube Sampling Algorithm Quantiles in each parameter Samples permuted to bins Reducing correlations? Random sample placement within bins Uses Reduces variance from additive components Higher-order convergence for separable functions Incremental, Hierarchic Incremental options Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
10 Enhanced MC Control Variate Known Surrogate Quantity of interest q has correlated surrogate statistic q s Known mean q s E [q s ] c qqs E [(q q)(q s q s )] σ q σ qs Variance-reduced statistic E [q] = E [q αq s ] + E [αq s ] = E [s] s q αq s + α q s σ 2 s = σ 2 q 2αc qqs σ q σ qs + α 2 σ 2 q s Integrating s via MC sampling, α 1, q s q gives σ e[ q] 0. Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
11 Enhanced MC Sensitivity Derivative Enhancement Linear Surrogate Justification: Adjoints are cheap One linearization at input mean Adds one forward, one sensitivity solve q s (ξ) q( ξ) + q ξ ( ξ)(ξ ξ) Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
12 Enhanced MC Local Sensitivity Derivative Enhancement Algorithm Take any input sample set Evaluate forward and adjoint at each Adds one sensitivity solve per sample Linearize around each nearby sample Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
13 Enhanced MC Local Sensitivity Derivative Surrogate Nearest-Neighbor Partition Voronoi cell shapes, complex input PDFs require MC sampling of surrogate Surrogate samples are associated with the nearest true sample O (N s N ss ) naive search cost Search operations (and surrogate evaluation) are much cheaper than true sample evaluation Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
14 Enhanced MC Bias Problem Using every sample to construct surrogate? [ Ns ] E i=1 q(ξ i) q s (ξ i ) = 0 E [ q L] = q L s q May have systemic bias for any problem Huge error for high-dimensional benchmark problems Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
15 Enhanced MC Bias Problem Using every sample to construct surrogate? [ Ns ] E i=1 q(ξ i) q s (ξ i ) = 0 E [ q L] = q L s q May have systemic bias for any problem Huge error for high-dimensional benchmark problems Solution Subdivide sample set (e.g. 2, 4, 8 subsets) Use one subset to construct surrogate, remainder to integrate bias Repeat for all subsets; average. Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
16 Enhanced MC Bias Issues How many subsets? More subsets == larger N, reducing bias error Fewer subsets == smaller σ, reducing bias error Numerical results show dimension dependence What convergence rate to expect? Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
17 Results Visualizing.25 Million Trials Methodology 256 trials per case Dependent variable: mean(abs(error)) 32, 128, 512 true sample evaluations per trial 32, 128, 512 surrogate samples per true sample Statistics: mean, standard deviation Sampling: SRS, HLHS Methods: MC, SDEMC, LSDEMC2/4/8 Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
18 Results e-05 MC+SRS SDEMC+SRS LSDMC2+SRS LSDMC4+SRS LSDMC8+SRS MC+LHS SDEMC+LHS LSDMC2+LHS LSDMC4+LHS LSDMC8+LHS 1e Visualizing.25 Million Trials Methodology 256 trials per case Dependent variable: mean(abs(error)) 32, 128, 512 true sample evaluations per trial 32, 128, 512 surrogate samples per true sample Statistics: mean, standard deviation Sampling: SRS, HLHS Methods: MC, SDEMC, LSDEMC2/4/8 Graph Key Purple: MC, Red: SDEMC Blue/Cyan/Green: LSDEMC2/4/8 Error in Approximated Output Forward UQ Convergence: Mean X: SRS, O: LHS Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
19 Results Benchmark Problem: Smooth Normal Lognormal Distribution ξ (ξ 1,...ξ N ) ( ) µ ξ i N N, σ (N q(ξ) e i ξ i q Log-N (µ, σ) µ 1, σ 1 Arbitrary dimensionality N All parameters equally significant Simple analytic exact solution moments Variance, MC error independent of N Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
20 Results 1 Parameter 1 Forward UQ Convergence: Exp Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
21 Results 4 Parameters 1 Forward UQ Convergence: Exp Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
22 Results 16 Parameters 1 Forward UQ Convergence: Exp Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
23 Results 64 Parameters 1 Forward UQ Convergence: Exp Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
24 Results Benchmark Problem: C 0 abs Normal Folded Normal Distribution ξ (ξ 1,...ξ N ) ξ i N ( ) µ N, σ (N q(ξ) ξ i i q F N (µ, σ) µ 1, σ 1 Same benefits as previous benchmark Response function now piecewise linear Differentiable except on one hyperplane Derivative defined as 0 there Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
25 Results 1 Parameter Forward UQ Convergence: Abs Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output e Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
26 Results 4 Parameters 1 Forward UQ Convergence: Abs Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
27 Results 16 Parameters 1 Forward UQ Convergence: Abs Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
28 Results 64 Parameters 1 Forward UQ Convergence: Abs Benchmark, Mean MC+SRS SDEMC+SRS LSDEMC2+SRS LSDEMC4+SRS LSDEMC8+SRS MC+LHS SDEMC+LHS LSDEMC2+LHS LSDEMC4+LHS LSDEMC8+LHS Error in Approximated Output Number of Forward Evaluations Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
29 Results Future Improvements Anisotropic Voronoi metric Based on partial Hessian approximation? Smooth (multi-sample-based) surrogate? Questions? Roy H. Stogner, Vikram Garg LSDEMC Jul 27, / 24
Predictive Engineering and Computational Sciences. Full System Simulations. Algorithms and Uncertainty Quantification. Roy H.
PECOS Predictive Engineering and Computational Sciences Full System Simulations Algorithms and Uncertainty Quantification Roy H. Stogner The University of Texas at Austin October 12, 2011 Roy H. Stogner
Uncertainty Quantification and Validation Using RAVEN. A. Alfonsi, C. Rabiti. Risk-Informed Safety Margin Characterization. https://lwrs.inl.
Risk-Informed Safety Margin Characterization Uncertainty Quantification and Validation Using RAVEN https://lwrs.inl.gov A. Alfonsi, C. Rabiti North Carolina State University, Raleigh 06/28/2017 Assumptions
Estimating functional uncertainty using polynomial chaos and adjoint equations
0. Estimating functional uncertainty using polynomial chaos and adjoint equations February 24, 2011 1 Florida State University, Tallahassee, Florida, Usa 2 Moscow Institute of Physics and Technology, Moscow,
Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models
Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models Benjamin Peherstorfer a,, Boris Kramer a, Karen Willcox a a Department of Aeronautics
Uncertainty Quantification in Viscous Hypersonic Flows using Gradient Information and Surrogate Modeling
Uncertainty Quantification in Viscous Hypersonic Flows using Gradient Information and Surrogate Modeling Brian A. Lockwood, Markus P. Rumpfkeil, Wataru Yamazaki and Dimitri J. Mavriplis Mechanical Engineering
Risk Assessment for CO 2 Sequestration- Uncertainty Quantification based on Surrogate Models of Detailed Simulations
Risk Assessment for CO 2 Sequestration- Uncertainty Quantification based on Surrogate Models of Detailed Simulations Yan Zhang Advisor: Nick Sahinidis Department of Chemical Engineering Carnegie Mellon
Risk Analysis: Efficient Computation of Failure Probability
Risk Analysis: Efficient Computation of Failure Probability Nassim RAZAALY CWI - INRIA Bordeaux nassim.razaaly@inria.fr 20/09/2017 Nassim RAZAALY (INRIA-CWI) Tail Probability 20/09/2017 1 / 13 Motivation:
Experiences with Model Reduction and Interpolation
Experiences with Model Reduction and Interpolation Paul Constantine Stanford University, Sandia National Laboratories Qiqi Wang (MIT) David Gleich (Purdue) Emory University March 7, 2012 Joe Ruthruff (SNL)
Optimization Tools in an Uncertain Environment
Optimization Tools in an Uncertain Environment Michael C. Ferris University of Wisconsin, Madison Uncertainty Workshop, Chicago: July 21, 2008 Michael Ferris (University of Wisconsin) Stochastic optimization
Measure-Theoretic parameter estimation and prediction for contaminant transport and coastal ocean modeling
Measure-Theoretic parameter estimation and prediction for contaminant transport and coastal ocean modeling Steven Mattis and Lindley Graham RMSWUQ 2015 July 17, 2015 Collaborators 2/45 The University of
Generalized Information Reuse for Optimization Under Uncertainty with Non-Sample Average Estimators
Generalized Information Reuse for Optimization Under Uncertainty with Non-Sample Average Estimators Laurence W Cook, Jerome P Jarrett, Karen E Willcox June 14, 2018 Abstract In optimization under uncertainty
Suggestions for Making Useful the Uncertainty Quantification Results from CFD Applications
Suggestions for Making Useful the Uncertainty Quantification Results from CFD Applications Thomas A. Zang tzandmands@wildblue.net Aug. 8, 2012 CFD Futures Conference: Zang 1 Context The focus of this presentation
Model Calibration under Uncertainty: Matching Distribution Information
Model Calibration under Uncertainty: Matching Distribution Information Laura P. Swiler, Brian M. Adams, and Michael S. Eldred September 11, 008 AIAA Multidisciplinary Analysis and Optimization Conference
Predictive Engineering and Computational Sciences. Current Directions in libmesh Development. Roy H. Stogner
PECOS Predictive Engineering and Computational Sciences Current Directions in libmesh Development Roy H. Stogner Institute for Computational Engineering and Sciences The University of Texas at Austin May
Uncertainty Quantification in MEMS
Uncertainty Quantification in MEMS N. Agarwal and N. R. Aluru Department of Mechanical Science and Engineering for Advanced Science and Technology Introduction Capacitive RF MEMS switch Comb drive Various
Polynomial chaos expansions for structural reliability analysis
DEPARTMENT OF CIVIL, ENVIRONMENTAL AND GEOMATIC ENGINEERING CHAIR OF RISK, SAFETY & UNCERTAINTY QUANTIFICATION Polynomial chaos expansions for structural reliability analysis B. Sudret & S. Marelli Incl.
Gaussian Processes for Computer Experiments
Gaussian Processes for Computer Experiments Jeremy Oakley School of Mathematics and Statistics, University of Sheffield www.jeremy-oakley.staff.shef.ac.uk 1 / 43 Computer models Computer model represented
arxiv: v1 [stat.co] 24 Jul 2015
![arxiv: v1 [stat.co] 24 Jul 2015](/thumbs/89/97550853.jpg "arxiv: v1 [stat.co] 24 Jul 2015")
The generalization of Latin hypercube sampling Michael D. Shields and Jiaxin Zhang Department of Civil Engineering, Johns Hopkins University Corresponding Author: michael.shields@jhu.edu arxiv:1507.06716v1
Modeling with Itô Stochastic Differential Equations
Modeling with Itô Stochastic Differential Equations 2.4-2.6 E. Allen presentation by T. Perälä 27.0.2009 Postgraduate seminar on applied mathematics 2009 Outline Hilbert Space of Stochastic Processes (
Sobol-Hoeffding Decomposition with Application to Global Sensitivity Analysis
Sobol-Hoeffding decomposition Application to Global SA Computation of the SI Sobol-Hoeffding Decomposition with Application to Global Sensitivity Analysis Olivier Le Maître with Colleague & Friend Omar
Sequential Importance Sampling for Rare Event Estimation with Computer Experiments
Sequential Importance Sampling for Rare Event Estimation with Computer Experiments Brian Williams and Rick Picard LA-UR-12-22467 Statistical Sciences Group, Los Alamos National Laboratory Abstract Importance
Uncertainty Quantification in Viscous Hypersonic Flows using Gradient Information and Surrogate Modeling
Uncertainty Quantification in Viscous Hypersonic Flows using Gradient Information and Surrogate Modeling Brian A. Lockwood, Markus P. Rumpfkeil, Wataru Yamazaki, and Dimitri J. Mavriplis University of
A Polynomial Chaos Approach to Robust Multiobjective Optimization
A Polynomial Chaos Approach to Robust Multiobjective Optimization Silvia Poles 1, Alberto Lovison 2 1 EnginSoft S.p.A., Optimization Consulting Via Giambellino, 7 35129 Padova, Italy s.poles@enginsoft.it
Utilizing Adjoint-Based Techniques to Improve the Accuracy and Reliability in Uncertainty Quantification
Utilizing Adjoint-Based Techniques to Improve the Accuracy and Reliability in Uncertainty Quantification Tim Wildey Sandia National Laboratories Center for Computing Research (CCR) Collaborators: E. Cyr,
Multilevel stochastic collocations with dimensionality reduction
Multilevel stochastic collocations with dimensionality reduction Ionut Farcas TUM, Chair of Scientific Computing in Computer Science (I5) 27.01.2017 Outline 1 Motivation 2 Theoretical background Uncertainty
Uncertainty Quantification of EBR-II Loss of Heat Sink Simulations with SAS4A/SASSYS-1 and DAKOTA
1 IAEA-CN245-023 Uncertainty Quantification of EBR-II Loss of Heat Sink Simulations with SAS4A/SASSYS-1 and DAKOTA G. Zhang 1, T. Sumner 1, T. Fanning 1 1 Argonne National Laboratory, Argonne, IL, USA
Outline Introduction OLS Design of experiments Regression. Metamodeling. ME598/494 Lecture. Max Yi Ren
1 / 34 Metamodeling ME598/494 Lecture Max Yi Ren Department of Mechanical Engineering, Arizona State University March 1, 2015 2 / 34 1. preliminaries 1.1 motivation 1.2 ordinary least square 1.3 information
Keywords: Sonic boom analysis, Atmospheric uncertainties, Uncertainty quantification, Monte Carlo method, Polynomial chaos method.
Blucher Mechanical Engineering Proceedings May 2014, vol. 1, num. 1 www.proceedings.blucher.com.br/evento/10wccm SONIC BOOM ANALYSIS UNDER ATMOSPHERIC UNCERTAINTIES BY A NON-INTRUSIVE POLYNOMIAL CHAOS
On Nesterov s Random Coordinate Descent Algorithms
On Nesterov s Random Coordinate Descent Algorithms Zheng Xu University of Texas At Arlington February 19, 2015 1 Introduction Full-Gradient Descent Coordinate Descent 2 Random Coordinate Descent Algorithm
Is My CFD Mesh Adequate? A Quantitative Answer
Is My CFD Mesh Adequate? A Quantitative Answer Krzysztof J. Fidkowski Gas Dynamics Research Colloqium Aerospace Engineering Department University of Michigan January 26, 2011 K.J. Fidkowski (UM) GDRC 2011
Polynomial chaos expansions for sensitivity analysis
c DEPARTMENT OF CIVIL, ENVIRONMENTAL AND GEOMATIC ENGINEERING CHAIR OF RISK, SAFETY & UNCERTAINTY QUANTIFICATION Polynomial chaos expansions for sensitivity analysis B. Sudret Chair of Risk, Safety & Uncertainty
AN EFFICIENT COMPUTATIONAL FRAMEWORK FOR UNCERTAINTY QUANTIFICATION IN MULTISCALE SYSTEMS
AN EFFICIENT COMPUTATIONAL FRAMEWORK FOR UNCERTAINTY QUANTIFICATION IN MULTISCALE SYSTEMS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of
Gradient Enhanced Universal Kriging Model for Uncertainty Propagation in Nuclear Engineering
Gradient Enhanced Universal Kriging Model for Uncertainty Propagation in Nuclear Engineering Brian A. Lockwood 1 and Mihai Anitescu 2 1 Department of Mechanical Engineering University of Wyoming 2 Mathematics
Dinesh Kumar, Mehrdad Raisee and Chris Lacor
Dinesh Kumar, Mehrdad Raisee and Chris Lacor Fluid Mechanics and Thermodynamics Research Group Vrije Universiteit Brussel, BELGIUM dkumar@vub.ac.be; m_raisee@yahoo.com; chris.lacor@vub.ac.be October, 2014
Design for Reliability and Robustness through probabilistic Methods in COMSOL Multiphysics with OptiY
Presented at the COMSOL Conference 2008 Hannover Multidisciplinary Analysis and Optimization In1 Design for Reliability and Robustness through probabilistic Methods in COMSOL Multiphysics with OptiY In2
Safety Envelope for Load Tolerance and Its Application to Fatigue Reliability Design
Safety Envelope for Load Tolerance and Its Application to Fatigue Reliability Design Haoyu Wang * and Nam H. Kim University of Florida, Gainesville, FL 32611 Yoon-Jun Kim Caterpillar Inc., Peoria, IL 61656
Different Criteria for Active Learning in Neural Networks: A Comparative Study
Different Criteria for Active Learning in Neural Networks: A Comparative Study Jan Poland and Andreas Zell University of Tübingen, WSI - RA Sand 1, 72076 Tübingen, Germany Abstract. The field of active
Sampling versus optimization in very high dimensional parameter spaces
Sampling versus optimization in very high dimensional parameter spaces Grigor Aslanyan Berkeley Center for Cosmological Physics UC Berkeley Statistical Challenges in Modern Astronomy VI Carnegie Mellon
An introduction to Bayesian statistics and model calibration and a host of related topics
An introduction to Bayesian statistics and model calibration and a host of related topics Derek Bingham Statistics and Actuarial Science Simon Fraser University Cast of thousands have participated in the
Efficient sampling strategies to estimate extremely low probabilities
Efficient sampling strategies to estimate extremely low probabilities Cédric J. Sallaberry a*, Robert E. Kurth a a Engineering Mechanics Corporation of Columbus (Emc 2 ) Columbus, OH, USA Abstract: The
2.3 Estimating PDFs and PDF Parameters
.3 Estimating PDFs and PDF Parameters estimating means - discrete and continuous estimating variance using a known mean estimating variance with an estimated mean estimating a discrete pdf estimating a
Sparse polynomial chaos expansions in engineering applications
DEPARTMENT OF CIVIL, ENVIRONMENTAL AND GEOMATIC ENGINEERING CHAIR OF RISK, SAFETY & UNCERTAINTY QUANTIFICATION Sparse polynomial chaos expansions in engineering applications B. Sudret G. Blatman (EDF R&D,
arxiv: v1 [math.na] 14 Sep 2017
![arxiv: v1 [math.na] 14 Sep 2017](/thumbs/73/68871397.jpg "arxiv: v1 [math.na] 14 Sep 2017")
Stochastic collocation approach with adaptive mesh refinement for parametric uncertainty analysis arxiv:1709.04584v1 [math.na] 14 Sep 2017 Anindya Bhaduri a, Yanyan He 1b, Michael D. Shields a, Lori Graham-Brady
Multilevel Monte Carlo for uncertainty quantification in structural engineering
Multilevel Monte Carlo for uncertainty quantification in structural engineering P. Blondeel a,, P. Robbe a, C. Van hoorickx b, G. Lombaert b, S. Vandewalle a a KU Leuven, Department of Computer Science,
Uncertainty Quantification in Computational Science
DTU 2010 - Lecture I Uncertainty Quantification in Computational Science Jan S Hesthaven Brown University Jan.Hesthaven@Brown.edu Objective of lectures The main objective of these lectures are To offer
SENSITIVITY ANALYSIS IN NUMERICAL SIMULATION OF MULTIPHASE FLOW FOR CO 2 STORAGE IN SALINE AQUIFERS USING THE PROBABILISTIC COLLOCATION APPROACH
XIX International Conference on Water Resources CMWR 2012 University of Illinois at Urbana-Champaign June 17-22,2012 SENSITIVITY ANALYSIS IN NUMERICAL SIMULATION OF MULTIPHASE FLOW FOR CO 2 STORAGE IN
arxiv: v1 [stat.ap] 17 Jan 2019
![arxiv: v1 [stat.ap] 17 Jan 2019](/thumbs/93/114212238.jpg "arxiv: v1 [stat.ap] 17 Jan 2019")
Application of Stochastic and Deterministic Techniques for Uncertainty Quantification and Sensitivity Analysis of Energy Systems a Majdi I. Radaideh, b Mohammad I. Radaideh a Department of Nuclear, Plasma,
Scalable Algorithms for Optimal Control of Systems Governed by PDEs Under Uncertainty
Scalable Algorithms for Optimal Control of Systems Governed by PDEs Under Uncertainty Alen Alexanderian 1, Omar Ghattas 2, Noémi Petra 3, Georg Stadler 4 1 Department of Mathematics North Carolina State
Lecture 3: Adaptive Construction of Response Surface Approximations for Bayesian Inference
Lecture 3: Adaptive Construction of Response Surface Approximations for Bayesian Inference Serge Prudhomme Département de mathématiques et de génie industriel Ecole Polytechnique de Montréal SRI Center
EFFICIENT SHAPE OPTIMIZATION USING POLYNOMIAL CHAOS EXPANSION AND LOCAL SENSITIVITIES
9 th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability EFFICIENT SHAPE OPTIMIZATION USING POLYNOMIAL CHAOS EXPANSION AND LOCAL SENSITIVITIES Nam H. Kim and Haoyu Wang University
Support Vector Regression (SVR) Descriptions of SVR in this discussion follow that in Refs. (2, 6, 7, 8, 9). The literature
Support Vector Regression (SVR) Descriptions of SVR in this discussion follow that in Refs. (2, 6, 7, 8, 9). The literature suggests the design variables should be normalized to a range of [-1,1] or [0,1].
Markov Chain Monte Carlo Methods for Stochastic
Markov Chain Monte Carlo Methods for Stochastic Optimization i John R. Birge The University of Chicago Booth School of Business Joint work with Nicholas Polson, Chicago Booth. JRBirge U Florida, Nov 2013
CS 450 Numerical Analysis. Chapter 8: Numerical Integration and Differentiation
Lecture slides based on the textbook Scientific Computing: An Introductory Survey by Michael T. Heath, copyright c 2018 by the Society for Industrial and Applied Mathematics. http://www.siam.org/books/cl80
Sensitivity Analysis of a Nuclear Reactor System Finite Element Model
Westinghouse Non-Proprietary Class 3 Sensitivity Analysis of a Nuclear Reactor System Finite Element Model 2018 ASME Verification & Validation Symposium VVS2018-9306 Gregory A. Banyay, P.E. Stephen D.
MODIFIED MONTE CARLO WITH LATIN HYPERCUBE METHOD
MODIFIED MONTE CARLO WITH LATIN HYPERCUBE METHOD Latin hypercube sampling (LHS) was introduced by McKay, Conover and Beckman as a solution to increase the efficiency of computer simulations. This technique
UNCERTAINTY ESTIMATION IN SEISMIC COLLAPSE ASSESSMENT OF MODERN REINFORCED CONCRETE MOMENT FRAME BUILDINGS
10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska UNCERTAINTY ESTIMATION IN SEISMIC COLLAPSE ASSESSMENT OF MODERN REINFORCED
Uncertainty representation and propagation in chemical networks
Uncertainty representation and propagation in chemical networks P. Pernot Laboratoire de Chimie Physique, Orsay Plan 1 Introduction 2 Uncertainty propagation 3 Treatment of uncertainties for chemical rates
DAKOTA/UQ: A Toolkit For Uncertainty Quantification in a Multiphysics, Massively Parallel Computational Environment
DAKOTA/UQ: A Toolkit For Uncertainty Quantification in a Multiphysics, Massively Parallel Computational Environment Steven F. Wojtkiewicz sfwojtk@sandia.gov Structural Dynamics Research, Dept. 9124 Sandia-Albuquerque
Optimal Approximations of Coupling in Multidisciplinary Models
Optimal Approximations of Coupling in Multidisciplinary Models Ricardo Baptista, Youssef Marzouk, Karen Willcox, Massachusetts Institute of Technology, Cambridge, MA and Benjamin Peherstorfer University
Statistical Prediction Based on Censored Life Data. Luis A. Escobar Department of Experimental Statistics Louisiana State University.
Statistical Prediction Based on Censored Life Data Overview Luis A. Escobar Department of Experimental Statistics Louisiana State University and William Q. Meeker Department of Statistics Iowa State University
Random Eigenvalue Problems in Structural Dynamics: An Experimental Investigation
Random Eigenvalue Problems in Structural Dynamics: An Experimental Investigation S. Adhikari, A. Srikantha Phani and D. A. Pape School of Engineering, Swansea University, Swansea, UK Email: S.Adhikari@swansea.ac.uk
Uncertainty Propagation
Setting: Uncertainty Propagation We assume that we have determined distributions for parameters e.g., Bayesian inference, prior experiments, expert opinion Ṫ 1 = 1 - d 1 T 1 - (1 - ")k 1 VT 1 Ṫ 2 = 2 -
s-scattering Length by Bold DiagMC
s-scattering Length by Bold DiagMC For a 3D particle of the mass m in the potential U(r, the s-scattering length a can be expressed as the zeroth Fourier component of the pseudo-potential Ũ (we set h =
Introduction to Aspects of Multiscale Modeling as Applied to Porous Media
Introduction to Aspects of Multiscale Modeling as Applied to Porous Media Part II Todd Arbogast Department of Mathematics and Center for Subsurface Modeling, Institute for Computational Engineering and
Recent Probabilistic Computational Efficiency Enhancements in DARWIN TM
Recent Probabilistic Computational Efficiency Enhancements in DARWIN TM Luc Huyse & Michael P. Enright Southwest Research Institute Harry R. Millwater University of Texas at San Antonio Simeon H.K. Fitch
MEASUREMENT UNCERTAINTY AND SUMMARISING MONTE CARLO SAMPLES
XX IMEKO World Congress Metrology for Green Growth September 9 14, 212, Busan, Republic of Korea MEASUREMENT UNCERTAINTY AND SUMMARISING MONTE CARLO SAMPLES A B Forbes National Physical Laboratory, Teddington,
Uncertainty Quantification in Performance Evaluation of Manufacturing Processes
Uncertainty Quantification in Performance Evaluation of Manufacturing Processes Manufacturing Systems October 27, 2014 Saideep Nannapaneni, Sankaran Mahadevan Vanderbilt University, Nashville, TN Acknowledgement
Chaospy: A modular implementation of Polynomial Chaos expansions and Monte Carlo methods
Chaospy: A modular implementation of Polynomial Chaos expansions and Monte Carlo methods Simen Tennøe Supervisors: Jonathan Feinberg Hans Petter Langtangen Gaute Einevoll Geir Halnes University of Oslo,
Chapter 9. Non-Parametric Density Function Estimation
9-1 Density Estimation Version 1.2 Chapter 9 Non-Parametric Density Function Estimation 9.1. Introduction We have discussed several estimation techniques: method of moments, maximum likelihood, and least
Estimation of uncertainties using the Guide to the expression of uncertainty (GUM)
Estimation of uncertainties using the Guide to the expression of uncertainty (GUM) Alexandr Malusek Division of Radiological Sciences Department of Medical and Health Sciences Linköping University 2014-04-15
Adaptive surrogate modeling for response surface approximations with application to bayesian inference
Prudhomme and Bryant Adv. Model. and Simul. in Eng. Sci. 2015 2:22 DOI 10.1186/s40323-015-0045-5 RESEARCH ARTICLE Open Access Adaptive surrogate modeling for response surface approximations with application
ASME 2013 IDETC/CIE 2013 Paper number: DETC A DESIGN ORIENTED RELIABILITY METHODOLOGY FOR FATIGUE LIFE UNDER STOCHASTIC LOADINGS
ASME 2013 IDETC/CIE 2013 Paper number: DETC2013-12033 A DESIGN ORIENTED RELIABILITY METHODOLOGY FOR FATIGUE LIFE UNDER STOCHASTIC LOADINGS Zhen Hu, Xiaoping Du Department of Mechanical & Aerospace Engineering
Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 2: Application to TRACE
Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 2: Application to TRACE Xu Wu a,*, Tomasz Kozlowski a, Hadi Meidani b and Koroush Shirvan c a Department
Uncertainty quantification via codimension one domain partitioning and a new concentration inequality
Uncertainty quantification via codimension one domain partitioning and a new concentration inequality Tim Sullivan, Ufuk Topcu, Mike McKerns & Houman Owhadi tjs@..., utopcu@..., mmckerns@...& owhadi@caltech.edu
Novel mathematical and statistical approaches to uncertainty evaluation:
Novel mathematical and statistical approaches to uncertainty evaluation: Best practice guide to uncertainty evaluation for computationally expensive models Deliverable 2.5.1 of Work Package WP2 (Uncertainty
Data Integration for Big Data Analysis for finite population inference
for Big Data Analysis for finite population inference Jae-kwang Kim ISU January 23, 2018 1 / 36 What is big data? 2 / 36 Data do not speak for themselves Knowledge Reproducibility Information Intepretation
DATA ASSIMILATION FOR FLOOD FORECASTING
DATA ASSIMILATION FOR FLOOD FORECASTING Arnold Heemin Delft University of Technology 09/16/14 1 Data assimilation is the incorporation of measurement into a numerical model to improve the model results
Review of the role of uncertainties in room acoustics
Review of the role of uncertainties in room acoustics Ralph T. Muehleisen, Ph.D. PE, FASA, INCE Board Certified Principal Building Scientist and BEDTR Technical Lead Division of Decision and Information
A Practical Guide to Sensitivity Analysis of a Large-scale Computer Simulation Model
South Texas Project Risk- Informed GSI- 191 Evaluation A Practical Guide to Sensitivity Analysis of a Large-scale Computer Simulation Model Document: STP- RIGSI191- ARAI.01 Revision: 2.1 Date: December
Classification: The rest of the story
U NIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN CS598 Machine Learning for Signal Processing Classification: The rest of the story 3 October 2017 Today s lecture Important things we haven t covered yet Fisher
Sampling and Low-Rank Tensor Approximations
Sampling and Low-Rank Tensor Approximations Hermann G. Matthies Alexander Litvinenko, Tarek A. El-Moshely +, Brunswick, Germany + MIT, Cambridge, MA, USA wire@tu-bs.de http://www.wire.tu-bs.de $Id: 2_Sydney-MCQMC.tex,v.3
Convergence Analysis and Criterion for Data Assimilation with Sensitivities from Monte Carlo Neutron Transport Codes
PHYSOR 2018: Reactor Physics paving the way towards more efficient systems Cancun, Mexico, April 22-26, 2018 Convergence Analysis and Criterion for Data Assimilation with Sensitivities from Monte Carlo
Understanding Uncertainty in Climate Model Components Robin Tokmakian Naval Postgraduate School
Understanding Uncertainty in Climate Model Components Robin Tokmakian Naval Postgraduate School rtt@nps.edu Collaborators: P. Challenor National Oceanography Centre, UK; Jim Gattiker Los Alamos National
Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized Polynomial Chaos
49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 6t 7 - April 28, Schaumburg, IL AIAA 28-892 Evaluation of Non-Intrusive Approaches for Wiener-Askey Generalized
Predictive Engineering and Computational Sciences. Research Challenges in VUQ. Robert Moser. The University of Texas at Austin.
PECOS Predictive Engineering and Computational Sciences Research Challenges in VUQ Robert Moser The University of Texas at Austin March 2012 Robert Moser 1 / 9 Justifying Extrapolitive Predictions Need
A nonlinear filtering tool for analysis of hot-loop test campaings
A nonlinear filtering tool for analysis of hot-loop test campaings Enso Ikonen* Jenő Kovács*, ** * Systems Engineering Laboratory, Department of Process and Environmental Engineering, University of Oulu,
SeDFAM: Semiconductor Demand Forecast Accuracy Model
UTDallas.edu/ Metin SeDFAM: Semiconductor Demand Forecast Accuracy Model Metin Çakanyıldırım School of Management University of Texas at Dallas Robin Roundy School of Operations Research Cornell University
THE ROLE OF SENSITIVITY ANALYSIS IN MODEL IMPROVEMENT
Energy and Resources Research Institute School of something FACULTY OF OTHER Faculty of Engineering THE ROLE OF SENSITIVITY ANALYSIS IN MODEL IMPROVEMENT Alison S. Tomlin Michael Davis, Rex Skodje, Frédérique
However, reliability analysis is not limited to calculation of the probability of failure.
Probabilistic Analysis probabilistic analysis methods, including the first and second-order reliability methods, Monte Carlo simulation, Importance sampling, Latin Hypercube sampling, and stochastic expansions
Univariate Statistics (One Variable) : the Basics. Linear Regression Assisted by ANOVA Using Excel.
Where are we in the grand scheme? Univariate Statistics (One Variable) : the Basics Examples of Calculations Made Using Excel. Analysis of Variance (ANOVA). ANOVA Using Excel. Introduction to Linear Regression.
Noise Analysis of Regularized EM for SPECT Reconstruction 1
Noise Analysis of Regularized EM for SPECT Reconstruction Wenli Wang and Gene Gindi Departments of Electrical Engineering and Radiology SUNY at Stony Brook, Stony Brook, NY 794-846 Abstract The ability
Random Eigenvalue Problems Revisited
Random Eigenvalue Problems Revisited S Adhikari Department of Aerospace Engineering, University of Bristol, Bristol, U.K. Email: S.Adhikari@bristol.ac.uk URL: http://www.aer.bris.ac.uk/contact/academic/adhikari/home.html
variability and their application for environment protection
Main factors of climate variability and their application for environment protection problems in Siberia Vladimir i Penenko & Elena Tsvetova Institute of Computational Mathematics and Mathematical Geophysics
Adaptive Collocation with Kernel Density Estimation
Examples of with Kernel Density Estimation Howard C. Elman Department of Computer Science University of Maryland at College Park Christopher W. Miller Applied Mathematics and Scientific Computing Program
Machine Learning I Continuous Reinforcement Learning
Machine Learning I Continuous Reinforcement Learning Thomas Rückstieß Technische Universität München January 7/8, 2010 RL Problem Statement (reminder) state s t+1 ENVIRONMENT reward r t+1 new step r t
Reliability prediction for structures under cyclic loads and recurring inspections
Alberto W. S. Mello Jr* Institute of Aeronautics and Space São José dos Campos - Brazil amello@iae.cta.br Daniel Ferreira V. Mattos Institute of Aeronautics and Space São José dos Campos - Brazil daniel.ferreira@iae.cta.br
STAT232B Importance and Sequential Importance Sampling
STAT232B Importance and Sequential Importance Sampling Gianfranco Doretto Andrea Vedaldi June 7, 2004 1 Monte Carlo Integration Goal: computing the following integral µ = h(x)π(x) dx χ Standard numerical
arxiv: v1 [stat.ap] 26 Dec 2016
![arxiv: v1 [stat.ap] 26 Dec 2016](/thumbs/89/101192074.jpg "arxiv: v1 [stat.ap] 26 Dec 2016")
Noname manuscript No. (will be inserted by the editor) Orbit Uncertainty Propagation and Sensitivity Analysis With Separated Representations Marc Balducci Brandon Jones Alireza Doostan arxiv:1612.8423v1
Introduction to Uncertainty Quantification in Computational Science Handout #3
Introduction to Uncertainty Quantification in Computational Science Handout #3 Gianluca Iaccarino Department of Mechanical Engineering Stanford University June 29 - July 1, 2009 Scuola di Dottorato di
Parameter Selection Techniques and Surrogate Models
Parameter Selection Techniques and Surrogate Models Model Reduction: Will discuss two forms Parameter space reduction Surrogate models to reduce model complexity Input Representation Local Sensitivity