Uncertainty Quantification in Simulation Science

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1 Uncertainty Quantification in Simulation Science George Em Karniadakis Division of Applied Mathematics, Brown University & Department of Mechanical Engineering, MIT & Pacific Northwest National Labs, CM4/DoE The CRUNCH group:

2 Drag Crisis: Effect of Freestream Turbulence

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4 DNS vs. Experiment Ma & Karniadakis JFM, 2000 Cross-Flow Velocity: Energy spectrum at X/D=7 100 M DOF Intrinsic stochasticity -5/3 Black: DNS Blue: Experiment By Ong & Wallace Energy input (wave number)

5 DNS vs. Experiment Ma & Karniadakis JFM, 2000 Cross-Flow Velocity: Energy spectrum at X/D=7 100 M DOF Intrinsic stochasticity -5/3 Black: DNS Blue: Experiment By Ong & Wallace Energy input (wave number)

6 HPC Performance Development Over the Last 20 Years from Top500 Credit: Jack Dongarra, May

7 Prediction versus Postdiction High Performance Computing: Are we computing the wrong answers faster?

8 Verification, Validation and Uncertainty Quantification: A cross-cutting theme in Simulation First addressed rigorously by the Society for Computer Simulation (1979) MUNA: (Minimization and Management of Uncertainty in Numerical Aerodynamics): DLR, 8 Universities, Airbus Germany, Eurocopter, EADS-MAS (2007)

9 Multiscale Modeling of the Human Arterial Tree With Subra Suresh, MIT/NSF/CMU

10 The Multiscale Brain Fedosov et al, PNAS, January & July, 2011 Fedosov APS Metropolis award for best PhD, 2011 Grinberg et al., Gordon Bell finalist, SC 11

11 Traumatic Brain Injury (TBI) Work at MIT & MGH by: Thibault Prevost, Subra Suresh and Simona Socrate Supported by US Army

12 Arterial Wall Mechanics (Zohar Yosibash, Ben Gurion) Load cell Micrometer Stress vs stretch 5 ITA s segments produce different response.

13 Energy equations : D Dt MHD Governing Equations : Non-equilibrium Plasma e D Dt D i Dt P V ( T ) P V J E ( R e 4 3 R i V ( R e i T ) T e R i ) er er ei,,, Ions Electrons Radiation d i Cv dt i, d e Cv dte i e Generalized Ohm s law : me J 2 N e t where e E V B 1 Pe N e e mef 2 e N e J B N ec e J,

14 Uncertainty in Equation of State: Teflon Turchi et al. AIAA MACH2 RESULTS Need For: Stochastic Simulations

15 UQ Across Length Scales Uncertainty in initial and/or boundary (operating) conditions at the macro scale + Uncertain heat flux on the nozzle flap Limited information about the microstructure of the material Topological uncertainty at lower scales How do mechanical properties and damage evolve? Will the device fail? With what probability? - Simple one way coupling: Upscale the property statistics to the macro scale and use to compute statistics - Two way coupling: For tightly coupled problems, solve micromacro stochastic PDEs simultaneously. Need information theoretic models to propagate uncertainty across scales Credit: N. Zabaras,

16 Sources of Uncertainty (There are many faces to the mask of uncertainty - Richard Bellman) Discretization Error/Code Uncertainty: spatio/temporal resolution, sampling; round-off; random-number generation; system errors. Parameter Uncertainty: inputs as unknown parameters of the model; specific applications or global parameters with common values over a range of contexts or even in all contexts. Parametric Variability: model parameters are left unspecified, e.g., in risk analysis; measurement errors; inherent stochasticity. Model Inadequacy: non-parametric uncertainty; difference between the true mean values of the real-world process and the code output at the true values of the inputs. 16 Kennedy & O Hagan, 2001

17 Autonomy and Uncertainty in Robotics MIT Aachen

18 All-Electric-Ship for US Navy: Gas Turbine-Synchronous Machine-Bus-Resistor Uncertainty: 50% on Speed Governor of GT; step change of load at t=20 s Gas Turbine GT Exciter SM V s 21 MW Constant Load 3-phase Resistor Load Torque 3-phase, 60 Hz 21 MW Synchronous Generator Harmonic Filter 3-phase, 4160 V AC Distribution Bus Uncertainty is Very important during transients

19 Validation Hierarchy for a Hypersonic Cruise Missile

20 Finding: Industry needs more accurate Validation Pyramids Case study: Failure of the A-380 wing (February 14, 2006) Babuska et al., 2007 The wing had to endure 150% of the load for 3 sec but it broke at 147%. The wing failed because a key validation experiment was not included in the Pyramid Design of a new Validation Pyramid

21 Application Areas Atomistic model Averaged properties Continuum model Microstructure 21

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23 Research Areas I. Mathematical Analysis and Multiscale Formulation of SPDEs (Brown-Caltech-Cornell) II. Numerical Solution of SPDEs (Brown-Cornell-Caltech) III. Dimension Reduction (MIT-Cornell-Brown) IV. Multiscale Property Estimation (Cornell-MIT-Brown) V. Design & Control Under Uncertainty (MIT-Cornell-Brown) 23

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25 Nature permits us to calculate only probabilities, yet science has not collapsed

26 UQ-Open Issues in Simulation Science HOLY GRAIL: UQ of Interacting (Multiphysics/Multiscale) Systems Non-parametric (Model) Uncertainty UQ in Multi-fidelity models UQ in Hybrid PDE-Molecular systems

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