Optimisation under Uncertainty with Stochastic PDEs for the History Matching Problem in Reservoir Engineering
|
|
|
- Cornelia Norris
- 5 years ago
- Views:
Transcription
1 Optimisation under Uncertainty with Stochastic PDEs for the History Matching Problem in Reservoir Engineering Hermann G. Matthies Technische Universität Braunschweig
2 Overall Problem 2 Motivation: Computational tools for uncertainty quantification Situation: Geostatistical model with stochastic uncertainty and physical/ mathematical flow model Identification: History matching of well production data Goal: Predict well production and uncertainty Reservoir Long Term Goal: Optimal control of well production under uncertainty
3 Physical / Mathematical / Stochastic Model 3 Physical: multiphase flow in porous media (Darcy, Buckley-Leverett,...) Mathematical: coupled PDEs, conservation and transport/constitutive laws C t w + A(w) = g Stochastic: Prior geostatistic model of data and stochastic sources/sinks uncertainty. Simple Example: Darcy flow with stochastic coefficients c t u (κ u) = f Goal is the prediction of functional of future state u and its uncertainty. Explicit modelling and quantificaton of uncertainty. System identification under prior uncertainty and observed data. Predict future state and quantify uncertainty given posteriori model. Long term goal: Optimal Control of well yields.
4 Partly Open Problems 4 General Formulation: Coherent stochastic forward / inverse problem formulation, adequate type of identfication, geostatistical (non-gaussian) models. Forward Problem: Fast SPDE solvers based on stochastic Galerkin methods, much faster than Monte Carlo. Inverse Problem: Efficient solvers for nonlinear stochastic problem. Error Control: combined ( spatial & stochastic) error estimates and adaptivity. Uncertainty: Efficient quantification, high-dimensional integration. Software: Modular, independent, software management conformity. Long Term: Optimal learning / adaptive control.
5 Novel SPDE Techniques 5 General: Functional analytic formulation of stochastic problem, white noise analysis, Malliavin calculus. Solver: Stochastic Galerkin via polynomial chaos, tensor product solver, combination with fast deterministic solvers, low-rank approximation, Karhunen- Loève (POD, SVD), model reduction, efficient parallelisation. Error Control: Goal oriented, dual weighted residual (DWR), adjoint methods. Uncertainty: High-dimensional integration, sparse grids Smolyak methods. Other: Standard state of the art techniques, FEM/FVM & FDM spatial/ temporal discretisation, fast (multilevel) deterministic solvers x Mean x y y 1 1 Standard Deviation x y 1 1 Pr{u(x) > 8}
6 System Identification Approaches 6 Approaches for system identification Maximum Likelihood: find most likely point. Bayesian like update of prior information based on observation stochastic posterior. Least Squares in equilibrium equation. Constitutive relation error CRE Separate certain (conservation: c u t + q = f) from uncertain assumptions (CR: q = κ u). Realisation Kalman filter EnKF Ensemble (via Monte Carlo) Kalman filtering.
7 Problem Sequence 7 Sequence of problems with increasing difficulty: linear diffusion: Darcy flow with stochastic conductivity stochastic non-gaussian velocity field. diffusion / advection: Solute transport (single phase) with stochastic velocity and (anomalous) dispersion. non-linear multi-phase flow, water air. Simulation NAPL multi-phase flow oil gas water...
8 Software Framework 8 Loose software coupling: Modular, independent parts. Software engineering: Components communicate via middleware. Tight numerical coupling: Integration of components into overall numerical scheme. Middleware: Component Template Library (CTL), allows distributed / coarse grain parallelisation. Optimiser Platon FEM ParaFep Eigenvalue (P)Arpack Communication Middleware CTL Component Template Library (MPI, PVM, TCP IP, etc...) Software KLE PCE StoFEL KLE StoFEL PCE Tensor Product Solver StoFEL PS
9 Related Collaboration / Work 9 Numerical / stochastic upscaling: Helmig IWS Uni Stuttgart; Cirpka ETH Zürich; Kulasiri Lincoln University, Christchurch. Stochastic material properties, error estimates: Ibrahimbegović, Ladevèze LMT ENS Cachan/ Paris; Villon UTC Compiegne; Wriggers IBNM Uni Hannover; Carstensen HU Berlin. Numerics for SPDEs: Schwab ETH Zürich; Tempone Florida State University; Babuška U of Texas, Austin; Burrage U of Queensland, Brisbane. System Identification: Faßbender. Coupled Problems: Ohayon CNAM, Paris. Software framework for history matching: Scandpower, Hamburg. Please visit poster early, I have to teach tomorrow morning.
Parametric Problems, Stochastics, and Identification
Parametric Problems, Stochastics, and Identification Hermann G. Matthies a B. Rosić ab, O. Pajonk ac, A. Litvinenko a a, b University of Kragujevac c SPT Group, Hamburg wire@tu-bs.de http://www.wire.tu-bs.de
Numerical Approximation of Stochastic Elliptic Partial Differential Equations
Numerical Approximation of Stochastic Elliptic Partial Differential Equations Hermann G. Matthies, Andreas Keese Institut für Wissenschaftliches Rechnen Technische Universität Braunschweig wire@tu-bs.de
Hierarchical Parallel Solution of Stochastic Systems
Hierarchical Parallel Solution of Stochastic Systems Second M.I.T. Conference on Computational Fluid and Solid Mechanics Contents: Simple Model of Stochastic Flow Stochastic Galerkin Scheme Resulting Equations
Quantifying Uncertainty: Modern Computational Representation of Probability and Applications
Quantifying Uncertainty: Modern Computational Representation of Probability and Applications Hermann G. Matthies with Andreas Keese Technische Universität Braunschweig wire@tu-bs.de http://www.wire.tu-bs.de
Partial Differential Equations with Stochastic Coefficients
Partial Differential Equations with Stochastic Coefficients Hermann G. Matthies gemeinsam mit Andreas Keese Institut für Wissenschaftliches Rechnen Technische Universität Braunschweig wire@tu-bs.de http://www.wire.tu-bs.de
Stochastic Collocation Methods for Polynomial Chaos: Analysis and Applications
Stochastic Collocation Methods for Polynomial Chaos: Analysis and Applications Dongbin Xiu Department of Mathematics, Purdue University Support: AFOSR FA955-8-1-353 (Computational Math) SF CAREER DMS-64535
At A Glance. UQ16 Mobile App.
At A Glance UQ16 Mobile App Scan the QR code with any QR reader and download the TripBuilder EventMobile app to your iphone, ipad, itouch or Android mobile device. To access the app or the HTML 5 version,
At-A-Glance SIAM Events Mobile App
At-A-Glance SIAM Events Mobile App Scan the QR code with any QR reader and download the TripBuilder EventMobile app to your iphone, ipad, itouch or Android mobile device.you can also visit www.tripbuildermedia.com/apps/siamevents
Sampling and low-rank tensor approximation of the response surface
Sampling and low-rank tensor approximation of the response surface tifica Alexander Litvinenko 1,2 (joint work with Hermann G. Matthies 3 ) 1 Group of Raul Tempone, SRI UQ, and 2 Group of David Keyes,
Monte Carlo Methods for Uncertainty Quantification
Monte Carlo Methods for Uncertainty Quantification Mike Giles Mathematical Institute, University of Oxford Contemporary Numerical Techniques Mike Giles (Oxford) Monte Carlo methods 1 / 23 Lecture outline
A Spectral Approach to Linear Bayesian Updating
A Spectral Approach to Linear Bayesian Updating Oliver Pajonk 1,2, Bojana V. Rosic 1, Alexander Litvinenko 1, and Hermann G. Matthies 1 1 Institute of Scientific Computing, TU Braunschweig, Germany 2 SPT
Introduction to Computational Stochastic Differential Equations
Introduction to Computational Stochastic Differential Equations Gabriel J. Lord Catherine E. Powell Tony Shardlow Preface Techniques for solving many of the differential equations traditionally used by
NON-LINEAR APPROXIMATION OF BAYESIAN UPDATE
tifica NON-LINEAR APPROXIMATION OF BAYESIAN UPDATE Alexander Litvinenko 1, Hermann G. Matthies 2, Elmar Zander 2 http://sri-uq.kaust.edu.sa/ 1 Extreme Computing Research Center, KAUST, 2 Institute of Scientific
Organization. I MCMC discussion. I project talks. I Lecture.
Organization I MCMC discussion I project talks. I Lecture. Content I Uncertainty Propagation Overview I Forward-Backward with an Ensemble I Model Reduction (Intro) Uncertainty Propagation in Causal Systems
MULTISCALE FINITE ELEMENT METHODS FOR STOCHASTIC POROUS MEDIA FLOW EQUATIONS AND APPLICATION TO UNCERTAINTY QUANTIFICATION
MULTISCALE FINITE ELEMENT METHODS FOR STOCHASTIC POROUS MEDIA FLOW EQUATIONS AND APPLICATION TO UNCERTAINTY QUANTIFICATION P. DOSTERT, Y. EFENDIEV, AND T.Y. HOU Abstract. In this paper, we study multiscale
Stochastic Finite Elements: Computational Approaches to SPDEs
Stochastic Finite Elements: Computational Approaches to SPDEs Hermann G. Matthies Andreas Keese, Elmar Zander, Alexander Litvinenko, Bojana Rosić Technische Universität Braunschweig wire@tu-bs.de http://www.wire.tu-bs.de
Gaussian Process Approximations of Stochastic Differential Equations
Gaussian Process Approximations of Stochastic Differential Equations Cédric Archambeau Centre for Computational Statistics and Machine Learning University College London c.archambeau@cs.ucl.ac.uk CSML
On a Data Assimilation Method coupling Kalman Filtering, MCRE Concept and PGD Model Reduction for Real-Time Updating of Structural Mechanics Model
On a Data Assimilation Method coupling, MCRE Concept and PGD Model Reduction for Real-Time Updating of Structural Mechanics Model 2016 SIAM Conference on Uncertainty Quantification Basile Marchand 1, Ludovic
Implementation of Sparse Wavelet-Galerkin FEM for Stochastic PDEs
Implementation of Sparse Wavelet-Galerkin FEM for Stochastic PDEs Roman Andreev ETH ZÜRICH / 29 JAN 29 TOC of the Talk Motivation & Set-Up Model Problem Stochastic Galerkin FEM Conclusions & Outlook Motivation
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
PRECONDITIONING MARKOV CHAIN MONTE CARLO SIMULATIONS USING COARSE-SCALE MODELS
PRECONDITIONING MARKOV CHAIN MONTE CARLO SIMULATIONS USING COARSE-SCALE MODELS Y. EFENDIEV, T. HOU, AND W. LUO Abstract. We study the preconditioning of Markov Chain Monte Carlo (MCMC) methods using coarse-scale
Stochastic Spectral Approaches to Bayesian Inference
Stochastic Spectral Approaches to Bayesian Inference Prof. Nathan L. Gibson Department of Mathematics Applied Mathematics and Computation Seminar March 4, 2011 Prof. Gibson (OSU) Spectral Approaches to
Galerkin Methods for Linear and Nonlinear Elliptic Stochastic Partial Differential Equations
ScientifiComputing Galerkin Methods for Linear and Nonlinear Elliptic Stochastic Partial Differential Equations Hermann G. Matthies, Andreas Keese Institute of Scientific Computing Technical University
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
Numerical Analysis of Elliptic PDEs with Random Coefficients
Numerical Analysis of Elliptic PDEs with Random Coefficients (Lecture I) Robert Scheichl Department of Mathematical Sciences University of Bath Workshop on PDEs with Random Coefficients Weierstrass Institute,
NONLOCALITY AND STOCHASTICITY TWO EMERGENT DIRECTIONS FOR APPLIED MATHEMATICS. Max Gunzburger
NONLOCALITY AND STOCHASTICITY TWO EMERGENT DIRECTIONS FOR APPLIED MATHEMATICS Max Gunzburger Department of Scientific Computing Florida State University North Carolina State University, March 10, 2011
Solving the Stochastic Steady-State Diffusion Problem Using Multigrid
Solving the Stochastic Steady-State Diffusion Problem Using Multigrid Tengfei Su Applied Mathematics and Scientific Computing Advisor: Howard Elman Department of Computer Science Sept. 29, 2015 Tengfei
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,
Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen
Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen PARAMetric UNCertainties, Budapest STOCHASTIC PROCESSES AND FIELDS Noémi Friedman Institut für Wissenschaftliches Rechnen, wire@tu-bs.de
Overview. Bayesian assimilation of experimental data into simulation (for Goland wing flutter) Why not uncertainty quantification?
Delft University of Technology Overview Bayesian assimilation of experimental data into simulation (for Goland wing flutter), Simao Marques 1. Why not uncertainty quantification? 2. Why uncertainty quantification?
INTERPOLATION AND UPDATE IN DYNAMIC DATA-DRIVEN APPLICATION SIMULATIONS
INTERPOLATION AND UPDATE IN DYNAMIC DATA-DRIVEN APPLICATION SIMULATIONS CRAIG C. DOUGLAS University of Kentucky, Department of Computer Science, 325 McVey Hall, Lexington, KY 4561 and Yale University,
Uncertainty updating in the description of heterogeneous materials
TECHNISCHE MECHANIK, 3, 1-3, (21), 211 226 submitted: October 31, 29 Uncertainty updating in the description of heterogeneous materials A. Kučerová, H. G. Matthies At a macroscopic scale, the details of
Multilevel Monte Carlo for two phase flow and transport in random heterogeneous porous media
Eidgenössische Technische Hochschule Zürich Ecole polytechnique fédérale de Zurich Politecnico federale di Zurigo Swiss Federal Institute of Technology Zurich Multilevel Monte Carlo for two phase flow
Dynamic Data Driven Simulations in Stochastic Environments
Computing 77, 321 333 (26) Digital Object Identifier (DOI) 1.17/s67-6-165-3 Dynamic Data Driven Simulations in Stochastic Environments C. Douglas, Lexington, Y. Efendiev, R. Ewing, College Station, V.
Robust Ensemble Filtering With Improved Storm Surge Forecasting
Robust Ensemble Filtering With Improved Storm Surge Forecasting U. Altaf, T. Buttler, X. Luo, C. Dawson, T. Mao, I.Hoteit Meteo France, Toulouse, Nov 13, 2012 Project Ensemble data assimilation for storm
Schwarz Preconditioner for the Stochastic Finite Element Method
Schwarz Preconditioner for the Stochastic Finite Element Method Waad Subber 1 and Sébastien Loisel 2 Preprint submitted to DD22 conference 1 Introduction The intrusive polynomial chaos approach for uncertainty
Macroscopic Failure Analysis Based on a Random Field Representations Generated from Material Microstructures
Macroscopic Failure Analysis Based on a Random Field Representations Generated from Material Microstructures Reza Abedi Mechanical, Aerospace & Biomedical Engineering University of Tennessee Knoxville
A Posteriori Adaptive Low-Rank Approximation of Probabilistic Models
A Posteriori Adaptive Low-Rank Approximation of Probabilistic Models Rainer Niekamp and Martin Krosche. Institute for Scientific Computing TU Braunschweig ILAS: 22.08.2011 A Posteriori Adaptive Low-Rank
Lecture 1: Center for Uncertainty Quantification. Alexander Litvinenko. Computation of Karhunen-Loeve Expansion:
tifica Lecture 1: Computation of Karhunen-Loeve Expansion: Alexander Litvinenko http://sri-uq.kaust.edu.sa/ Stochastic PDEs We consider div(κ(x, ω) u) = f (x, ω) in G, u = 0 on G, with stochastic coefficients
Bayesian parameter estimation in predictive engineering
Bayesian parameter estimation in predictive engineering Damon McDougall Institute for Computational Engineering and Sciences, UT Austin 14th August 2014 1/27 Motivation Understand physical phenomena Observations
Reactive Transport in Porous Media
Reactive Transport in Porous Media Daniel M. Tartakovsky Department of Mechanical & Aerospace Engineering University of California, San Diego Alberto Guadagnini, Politecnico di Milano, Italy Peter C. Lichtner,
Gaussian Process Approximations of Stochastic Differential Equations
Gaussian Process Approximations of Stochastic Differential Equations Cédric Archambeau Dan Cawford Manfred Opper John Shawe-Taylor May, 2006 1 Introduction Some of the most complex models routinely run
Sequential Monte Carlo Samplers for Applications in High Dimensions
Sequential Monte Carlo Samplers for Applications in High Dimensions Alexandros Beskos National University of Singapore KAUST, 26th February 2014 Joint work with: Dan Crisan, Ajay Jasra, Nik Kantas, Alex
Adaptive Posterior Approximation within MCMC
Adaptive Posterior Approximation within MCMC Tiangang Cui (MIT) Colin Fox (University of Otago) Mike O Sullivan (University of Auckland) Youssef Marzouk (MIT) Karen Willcox (MIT) 06/January/2012 C, F,
Probabilistic Collocation Method for Uncertainty Analysis of Soil Infiltration in Flood Modelling
Probabilistic Collocation Method for Uncertainty Analysis of Soil Infiltration in Flood Modelling Y. Huang 1,2, and X.S. Qin 1,2* 1 School of Civil & Environmental Engineering, Nanyang Technological University,
Uncertainty quantification of engineering systems using the multilevel Monte Carlo method
Uncertainty quantification of engineering systems using the multilevel Monte Carlo method Helena Juliette Thomasin Unwin Supervised by Dr. Garth N. Wells Department of Engineering, University of Cambridge
Bayesian Inverse problem, Data assimilation and Localization
Bayesian Inverse problem, Data assimilation and Localization Xin T Tong National University of Singapore ICIP, Singapore 2018 X.Tong Localization 1 / 37 Content What is Bayesian inverse problem? What is
Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter
WATER RESOURCES RESEARCH, VOL. 45,, doi:10.1029/2008wr007148, 2009 Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter George Saad 1 and Roger Ghanem 1
Ergodicity in data assimilation methods
Ergodicity in data assimilation methods David Kelly Andy Majda Xin Tong Courant Institute New York University New York NY www.dtbkelly.com April 15, 2016 ETH Zurich David Kelly (CIMS) Data assimilation
Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model. David Darmon, AMSC Kayo Ide, AOSC, IPST, CSCAMM, ESSIC
Lagrangian Data Assimilation and Manifold Detection for a Point-Vortex Model David Darmon, AMSC Kayo Ide, AOSC, IPST, CSCAMM, ESSIC Background Data Assimilation Iterative process Forecast Analysis Background
Homogenization Theory
Homogenization Theory Sabine Attinger Lecture: Homogenization Tuesday Wednesday Thursday August 15 August 16 August 17 Lecture Block 1 Motivation Basic Ideas Elliptic Equations Calculation of Effective
Assessing the Value of Information from Inverse Modelling for Optimising Long-Term Oil Reservoir Performance
Assessing the Value of Information from Inverse Modelling for Optimising Long-Term Oil Reservoir Performance Eduardo Barros, TU Delft Paul Van den Hof, TU Eindhoven Jan Dirk Jansen, TU Delft 1 Oil & gas
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
Ensemble Kalman filter assimilation of transient groundwater flow data via stochastic moment equations
Ensemble Kalman filter assimilation of transient groundwater flow data via stochastic moment equations Alberto Guadagnini (1,), Marco Panzeri (1), Monica Riva (1,), Shlomo P. Neuman () (1) Department of
A Stochastic Collocation based. for Data Assimilation
A Stochastic Collocation based Kalman Filter (SCKF) for Data Assimilation Lingzao Zeng and Dongxiao Zhang University of Southern California August 11, 2009 Los Angeles Outline Introduction SCKF Algorithm
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,
The Ensemble Kalman Filter:
p.1 The Ensemble Kalman Filter: Theoretical formulation and practical implementation Geir Evensen Norsk Hydro Research Centre, Bergen, Norway Based on Evensen, Ocean Dynamics, Vol 5, No p. The Ensemble
The Ensemble Kalman Filter:
p.1 The Ensemble Kalman Filter: Theoretical formulation and practical implementation Geir Evensen Norsk Hydro Research Centre, Bergen, Norway Based on Evensen 23, Ocean Dynamics, Vol 53, No 4 p.2 The Ensemble
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
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
Error Budgets: A Path from Uncertainty Quantification to Model Validation
Error Budgets: A Path from Uncertainty Quantification to Model Validation Roger Ghanem Aerospace and Mechanical Engineering Civil Engineering University of Southern California Los Angeles Advanced Simulation
A regularized least-squares method for sparse low-rank approximation of multivariate functions
Workshop Numerical methods for high-dimensional problems April 18, 2014 A regularized least-squares method for sparse low-rank approximation of multivariate functions Mathilde Chevreuil joint work with
Development of Stochastic Artificial Neural Networks for Hydrological Prediction
Development of Stochastic Artificial Neural Networks for Hydrological Prediction G. B. Kingston, M. F. Lambert and H. R. Maier Centre for Applied Modelling in Water Engineering, School of Civil and Environmental
A Note on the Particle Filter with Posterior Gaussian Resampling
Tellus (6), 8A, 46 46 Copyright C Blackwell Munksgaard, 6 Printed in Singapore. All rights reserved TELLUS A Note on the Particle Filter with Posterior Gaussian Resampling By X. XIONG 1,I.M.NAVON 1,2 and
Consistent Downscaling of Seismic Inversions to Cornerpoint Flow Models SPE
Consistent Downscaling of Seismic Inversions to Cornerpoint Flow Models SPE 103268 Subhash Kalla LSU Christopher D. White LSU James S. Gunning CSIRO Michael E. Glinsky BHP-Billiton Contents Method overview
Uncertainty Quantification and related areas - An overview
Uncertainty Quantification and related areas - An overview Alexander Litvinenko, talk given at Department of Mathematical Sciences, Durham University Bayesian Computational Statistics & Modeling, KAUST
Dynamic System Identification using HDMR-Bayesian Technique
Dynamic System Identification using HDMR-Bayesian Technique *Shereena O A 1) and Dr. B N Rao 2) 1), 2) Department of Civil Engineering, IIT Madras, Chennai 600036, Tamil Nadu, India 1) ce14d020@smail.iitm.ac.in
Uncertainty Quantification and hypocoercivity based sensitivity analysis for multiscale kinetic equations with random inputs.
Uncertainty Quantification and hypocoercivity based sensitivity analysis for multiscale kinetic equations with random inputs Shi Jin University of Wisconsin-Madison, USA Shanghai Jiao Tong University,
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
Probabilistic collocation and Lagrangian sampling for tracer transport in randomly heterogeneous porous media
Eidgenössische Technische Hochschule Zürich Ecole polytechnique fédérale de Zurich Politecnico federale di Zurigo Swiss Federal Institute of Technology Zurich Probabilistic collocation and Lagrangian sampling
UNCERTAINTY QUANTIFICATION IN LIQUID COMPOSITE MOULDING PROCESSES
UNCERTAINTY QUANTIFICATION IN LIQUID COMPOSITE MOULDING PROCESSES Bart Verleye 1, Dirk Nuyens 1, Andrew Walbran 3,2, and Ming Gan 2 1 Dept. Computer Science, KU Leuven, Celestijnenlaan 200A, B-3001 Leuven,
Polynomial Chaos and Karhunen-Loeve Expansion
Polynomial Chaos and Karhunen-Loeve Expansion 1) Random Variables Consider a system that is modeled by R = M(x, t, X) where X is a random variable. We are interested in determining the probability of the
Kernel-based Approximation. Methods using MATLAB. Gregory Fasshauer. Interdisciplinary Mathematical Sciences. Michael McCourt.
SINGAPORE SHANGHAI Vol TAIPEI - Interdisciplinary Mathematical Sciences 19 Kernel-based Approximation Methods using MATLAB Gregory Fasshauer Illinois Institute of Technology, USA Michael McCourt University
Seminar: Data Assimilation
Seminar: Data Assimilation Jonas Latz, Elisabeth Ullmann Chair of Numerical Mathematics (M2) Technical University of Munich Jonas Latz, Elisabeth Ullmann (TUM) Data Assimilation 1 / 28 Prerequisites Bachelor:
Uncertainty Quantification for multiscale kinetic equations with random inputs. Shi Jin. University of Wisconsin-Madison, USA
Uncertainty Quantification for multiscale kinetic equations with random inputs Shi Jin University of Wisconsin-Madison, USA Where do kinetic equations sit in physics Kinetic equations with applications
Winter 2019 Math 106 Topics in Applied Mathematics. Lecture 1: Introduction
Winter 2019 Math 106 Topics in Applied Mathematics Data-driven Uncertainty Quantification Yoonsang Lee (yoonsang.lee@dartmouth.edu) Lecture 1: Introduction 19 Winter M106 Class: MWF 12:50-1:55 pm @ 200
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,
Employing Model Reduction for Uncertainty Visualization in the Context of CO 2 Storage Simulation
Employing Model Reduction for Uncertainty Visualization in the Context of CO 2 Storage Simulation Marcel Hlawatsch, Sergey Oladyshkin, Daniel Weiskopf University of Stuttgart Problem setting - underground
Non-Intrusive Solution of Stochastic and Parametric Equations
Non-Intrusive Solution of Stochastic and Parametric Equations Hermann G. Matthies a Loïc Giraldi b, Alexander Litvinenko c, Dishi Liu d, and Anthony Nouy b a,, Brunswick, Germany b École Centrale de Nantes,
Stochastic Elastic-Plastic Finite Element Method for Performance Risk Simulations
Stochastic Elastic-Plastic Finite Element Method for Performance Risk Simulations Boris Jeremić 1 Kallol Sett 2 1 University of California, Davis 2 University of Akron, Ohio ICASP Zürich, Switzerland August
STOCHASTIC SAMPLING METHODS
STOCHASTIC SAMPLING METHODS APPROXIMATING QUANTITIES OF INTEREST USING SAMPLING METHODS Recall that quantities of interest often require the evaluation of stochastic integrals of functions of the solutions
Multilevel Sequential 2 Monte Carlo for Bayesian Inverse Problems
Jonas Latz 1 Multilevel Sequential 2 Monte Carlo for Bayesian Inverse Problems Jonas Latz Technische Universität München Fakultät für Mathematik Lehrstuhl für Numerische Mathematik jonas.latz@tum.de November
Gaussian Filtering Strategies for Nonlinear Systems
Gaussian Filtering Strategies for Nonlinear Systems Canonical Nonlinear Filtering Problem ~u m+1 = ~ f (~u m )+~ m+1 ~v m+1 = ~g(~u m+1 )+~ o m+1 I ~ f and ~g are nonlinear & deterministic I Noise/Errors
Analysis and Computation of Hyperbolic PDEs with Random Data
Analysis and Computation of Hyperbolic PDEs with Random Data Mohammad Motamed 1, Fabio Nobile 2,3 and Raúl Tempone 1 1 King Abdullah University of Science and Technology, Thuwal, Saudi Arabia 2 EPFL Lausanne,
Uncertainty Quantification for multiscale kinetic equations with high dimensional random inputs with sparse grids
Uncertainty Quantification for multiscale kinetic equations with high dimensional random inputs with sparse grids Shi Jin University of Wisconsin-Madison, USA Kinetic equations Different Q Boltmann Landau
Lagrangian Data Assimilation and Its Application to Geophysical Fluid Flows
Lagrangian Data Assimilation and Its Application to Geophysical Fluid Flows Laura Slivinski June, 3 Laura Slivinski (Brown University) Lagrangian Data Assimilation June, 3 / 3 Data Assimilation Setup:
Uncertainty analysis of large-scale systems using domain decomposition
Center for Turbulence Research Annual Research Briefs 2007 143 Uncertainty analysis of large-scale systems using domain decomposition By D. Ghosh, C. Farhat AND P. Avery 1. Motivation and objectives A
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 13: SEQUENTIAL DATA
PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 13: SEQUENTIAL DATA Contents in latter part Linear Dynamical Systems What is different from HMM? Kalman filter Its strength and limitation Particle Filter
A new Hierarchical Bayes approach to ensemble-variational data assimilation
A new Hierarchical Bayes approach to ensemble-variational data assimilation Michael Tsyrulnikov and Alexander Rakitko HydroMetCenter of Russia College Park, 20 Oct 2014 Michael Tsyrulnikov and Alexander
Ensemble Kalman Filter
Ensemble Kalman Filter Geir Evensen and Laurent Bertino Hydro Research Centre, Bergen, Norway, Nansen Environmental and Remote Sensing Center, Bergen, Norway The Ensemble Kalman Filter (EnKF) Represents
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
Autonomous Navigation for Flying Robots
Computer Vision Group Prof. Daniel Cremers Autonomous Navigation for Flying Robots Lecture 6.2: Kalman Filter Jürgen Sturm Technische Universität München Motivation Bayes filter is a useful tool for state
arxiv: v2 [math.na] 8 Sep 2017
![arxiv: v2 [math.na] 8 Sep 2017](/thumbs/92/110906822.jpg "arxiv: v2 [math.na] 8 Sep 2017")
arxiv:1704.06339v [math.na] 8 Sep 017 A Monte Carlo approach to computing stiffness matrices arising in polynomial chaos approximations Juan Galvis O. Andrés Cuervo September 3, 018 Abstract We use a Monte
Fundamentals of Data Assimila1on
014 GSI Community Tutorial NCAR Foothills Campus, Boulder, CO July 14-16, 014 Fundamentals of Data Assimila1on Milija Zupanski Cooperative Institute for Research in the Atmosphere Colorado State University
NEW ALGORITHMS FOR UNCERTAINTY QUANTIFICATION AND NONLINEAR ESTIMATION OF STOCHASTIC DYNAMICAL SYSTEMS. A Dissertation PARIKSHIT DUTTA
NEW ALGORITHMS FOR UNCERTAINTY QUANTIFICATION AND NONLINEAR ESTIMATION OF STOCHASTIC DYNAMICAL SYSTEMS A Dissertation by PARIKSHIT DUTTA Submitted to the Office of Graduate Studies of Texas A&M University
Stochastic collocation and mixed finite elements for flow in porous media
Stochastic collocation and mixed finite elements for flow in porous media Benjamin Ganis a, Hector Klie b, Mary F. Wheeler b, Tim Wildey b, Ivan Yotov a, and Dongxiao Zhang c a Department of Mathematics,
UNCERTAINTY ASSESSMENT USING STOCHASTIC REDUCED BASIS METHOD FOR FLOW IN POROUS MEDIA
UNCERTAINTY ASSESSMENT USING STOCHASTIC REDUCED BASIS METHOD FOR FLOW IN POROUS MEDIA A REPORT SUBMITTED TO THE DEPARTMENT OF ENERGY RESOURCES ENGINEERING OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT
Research Article Multiresolution Analysis for Stochastic Finite Element Problems with Wavelet-Based Karhunen-Loève Expansion
Mathematical Problems in Engineering Volume 2012, Article ID 215109, 15 pages doi:10.1155/2012/215109 Research Article Multiresolution Analysis for Stochastic Finite Element Problems with Wavelet-Based
Machine Learning. Probability Basics. Marc Toussaint University of Stuttgart Summer 2014
Machine Learning Probability Basics Basic definitions: Random variables, joint, conditional, marginal distribution, Bayes theorem & examples; Probability distributions: Binomial, Beta, Multinomial, Dirichlet,
Modelling Under Risk and Uncertainty
Modelling Under Risk and Uncertainty An Introduction to Statistical, Phenomenological and Computational Methods Etienne de Rocquigny Ecole Centrale Paris, Universite Paris-Saclay, France WILEY A John Wiley