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UQ for the Global Atmosphere Using Concurrent Samples UQ for the Global Atmosphere Using Concurrent Samples

UQ for the Global Atmosphere Using Concurrent Samples - PowerPoint Presentation

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UQ for the Global Atmosphere Using Concurrent Samples - PPT Presentation

Bill Spotz Sandia National Laboratories SIAM Conference on UQ April 5 2016 Thanks Jeff Fike SNL New Mexico Andy Salinger SNL New Mexico Irina Tezaur SNL California Eric Phipps SNL New Mexico ID: 675838

pressure samples generation time samples pressure time generation global physics albany performance solver velocity vertical horizontal atmosphere mesh database

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Presentation Transcript

Slide1

UQ for the Global Atmosphere Using Concurrent Samples

Bill Spotz, Sandia National LaboratoriesSIAM Conference on UQ, April 5, 2016Slide2

Thanks

Jeff Fike, SNL New MexicoAndy Salinger, SNL New MexicoIrina Tezaur

, SNL CaliforniaEric Phipps, SNL New Mexico2Slide3

Outline

Aeras, a next-generation global atmosphere modelNext generation capabilitiesSoftware infrastructureConcurrent samples

Leveraging embedded UQ technologiesSoftware infrastructureNumerical experimentSummary and Future Work

3Slide4

Aeras is a

Sandia LDRD project whose goal is to develop a “Next Generation Global Atmosphere Model”Utilize state-of-the-art librariesImplement proven dycore

numerics: spectral elements w/hyperviscosityDemonstrate physics parameterization with simple cloud physicsAeras leverages leading-edge, massively parallel, C++ computational technologies from Sandia:

Albany (multiphysics application code base)Trilinos (solvers, discretizations, meshing, coupling, perf portability, …)Dakota (optimization, uncertainty quantification)Next generation capabilities

Performance portability, enabled by the Kokkos (Trilinos) programming modelUncertainty quantification, enabled by Stokhos (Trilinos) intrusive stochastic UQ package, and Dakota4Slide5

5

Element Level Fill

Material Models

Sensitivities

Field Manager

Discretization Library

Remeshing

UQ Solver

Nonlinear Solver

Time Integration

Optimization

Objective Function

Local Fill

Mesh Database

Mesh Tools

I/O Management

Input File Parser

Utilities

UQ (sampling)

Parameter Studies

Mesh I/O

Optimization

Geometry Database

Discretizations

Derivative Tools

Adjoints

UQ / PCE

Propagation

Constraints

Error Estimates

Continuation

Constrained Solves

Sensitivity Analysis

Stability Analysis

V&V, Calibration

Parameter List

Verification

Visualization

PostProcessing

Adaptivity

Model Reduction

Memory Management

System Models

MultiPhysics Coupling

OUU, Reliability

Communicators

Partitioning

Load Balancing

Analysis Tools

(

black-box)

Physics Fill

Composite Physics

Data Structures

Direct Solvers

Linear Algebra

Architecture-

Dependent Kernels

Preconditioners

Iterative Solvers

Eigen Solver

System UQ

Analysis Tools

(

embedded)

Matrix Partitioning

Inline Meshing

MMS Source Terms

Grid Transfers

Quality Improvement

Mesh Database

Solution Database

Derivatives

Regression Testing

Bug Tracking

Version Control

Software Quality

Porting

Performance Testing

Code Coverage

Mailing Lists

Release Process

Unit Testing

Web Pages

Build System

Backups

Verification Tests

DOF map

Multi-Core

Accelerators

Linear Programming

Graph Algorithms

Data-Centric Algs

SVDs

Map-Reduce

Network ModelsSlide6

Software Infrastructure

6

Tpetra

Kokkos

Epetra

Trikota

Stokhos

Evaluators

Note:

global atmosphere models have specializations and optimizations not originally supported by Albany:

horizontal vs. vertical bias

need for shell elements

spectral elements

explicit time stepping

transient embedded UQSlide7

Albany Generic Physics Interface

7Slide8

Concurrent Samples

There is another generic template type that determines the mathematical scalar typeThis would typically be

double in practiceWe can specialize to be an Array<double>

Length of array equals number of samples to computeInitialization…Overload operatorsWe can now leverage common objectsMeshMatricesEtc…In theory, hardware that requires more data to perform efficiently, will

8Slide9

Governing Equations

Shallow Water Equations3D Hydrostatic Equations

9

 

 

Legend

Horizontal velocity

Vorticity

Coriolis parameter

Radial unit vector

Horizontal gradient operator

Geopotential

Atmospheric thickness

Vertical coordinate

Vertical velocity

Gas constant

Temperature

Virtual temperature

Pressure

Specific heat, constant pressure

Total pressure time derivative

Legend

Horizontal velocity

Vorticity

Coriolis parameter

Radial unit vector

Horizontal gradient operator

Geopotential

Atmospheric thickness

Vertical coordinate

Vertical velocity

Gas constant

Temperature

Virtual temperature

Pressure

Specific heat, constant pressure

Total pressure time derivativeSlide10

Numerical Approach

Quadrilateral spectral elements tile the surface of the sphereNode points = Gauss-Lobato points = quadrature points → diagonal mass matrixContinuous

GalerkinRunge-Kutta 4th order time stepping

Finite difference formulation in verticalHyperviscosity for stabilization10Slide11

Numerical Experiment

Shallow Water EquationsTest Case 5 [Williamson]Zonal Flow Over an Isolated MountainMountain height used as random input variable

For each experimentWe run concurrent samples of size nWe repeat, as necessary, to achieve an ensemble of size 32

Sensitivities of latitudinal velocity with respect to mountain heightSlide12

Numerical Experiment

12Slide13

Aside: Performance Portability

13Slide14

Summary

We have developed Aeras, a next-generation global atmosphere model, that leverages leading-edge computational technologies from Sandia National LaboratoriesAeras is built on top of Albany, a multi-physics finite element code that takes advantage of

Trilinos for high-performance computing solver technologies, and Dakota for optimization and uncertainty quantificationThrough a creative use of embedded UQ, we have achieve a

doubling of the efficiency of our shallow water solver by running ensemble samples concurrently14Slide15

Future Work

Upgrade from an older set of linear algebra classes (Epetra) to a newer package that supports C++ templates (Tpetra)This will allow using the latest version of

Aeras/Albany, which in turn will allow concurrent samples to be used in conjunction with:Our performance portability

effortsSpectral elements3D hydrostatic equations15