SOS 10 March 6-9, 2006

Algorithms for Scientific Computing

and Informatics

David E. WombleSandia National Laboratories

SOS10 March 6-9, 2006

SAND2006-1407C

SOS 10 March 6-9, 2006

The Forward Simulation Problem

System Design

Geometric Modeling

Meshing

Physics

Model Equations

Discretization

Partitioning and Mapping

Nonlinear solve

Linear solve

Time integration

Informatics and Visualization

Adapt

SOS 10 March 6-9, 2006

Drivers

• Physics– Multiscale

• Scale– Billions of unknowns– Coupled physics

• Quality– Mesh– Discretization

• Implementation– Code and framework complexity– Machine architectures

SOS 10 March 6-9, 2006

Drivers

• Interactions between components– Solvers with– Discretization with– Meshing with– Load balancing with– Error estimation with– …

• Example– Z-pinch simulations

Liner implosion

SOS 10 March 6-9, 2006

What’s Missing?

System Design

Geometric Modeling

Meshing

Physics

Model Equations

Discretization

Partitioning and Mapping

Nonlinear solve

Linear solve

Time integration

Informatics and Visualization

AdaptV&V

Data

SOS 10 March 6-9, 2006

Verification and Validation

• Right now, we are using an ad-hoc, black box approach– Convergence studies and MMS– Point-wise comparisons to experimental data

• Need– Integration of V&V with code design, i.e., designed in.

» Element library with error estimators» Symbolic manipulation of equations and automatic differentiation» Designed to be part of a V&V framework (not a stand-alone code) and must

allow some “intrusion” into the code (e.g., sensitivity calculations)– Algorithms

» Error estimators, statistical methods, input distributions and stochastic equations (including solvers)

– Presentation of results

• Problem– Established infrastructure– Need knowledgeable users working with analysts and developers

SOS 10 March 6-9, 2006

V&V

But What Do We Really Want To Do

System Design

Geometric Modeling

Meshing

Physics

Model Equations

Discretization

Partitioning and Mapping

Nonlinear solve

Linear solve

Time integration

Informatics and Visualization

AdaptOptimization

and UQ

Improved design and understanding

Data

SOS 10 March 6-9, 2006

Visualization

• Geometric information (current)– Large scale– Desktop

• Non-geometric information (future)– Aggregate information (many

simulations)– Risk and uncertainties

• “Data-mining”– Need to think about how people really

use information– Tools to help extract information

(“features”)– Integration with simulation

SOS 10 March 6-9, 2006

Optimization and UQ

• Can include V&V in this loop, but adds design and “understanding”

– Ensemble of “single-point runs insufficient– Need to design for system performance, not just assess system

performance

• Need integrated tools– Many of the same tools as for V&V (e.g., error estimation, sensitivity

analysis)– Identify critical phenomena (turning points, bifurcations points)– Rigorous exploration of design space– Integrated design and solvers

• Need multifidelity– Surrogate methods– Hierarchy of resolutions and scale/physics couplings

• More integration of tools (designed in)– Including V&V, meshing and visualization

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SOS 10 March 6-9, 2006

Dealing With Uncertainty

• Simply propagating distributions and quantifying errors is not enough

• We need to be able to incorporate experimental data to further reduce uncertainties

SOS 10 March 6-9, 2006

Model Real World

Data

What About The Informatics Problem?

System Design

Geometric Modeling

Meshing

Physics

Model Equations

Discretization

Informatics and Visualization

Partitioning and Mapping

Nonlinear solve

Linear solve

Time integrationAdaptOptimization

and UQ

Improved design and understanding

Processing ToolsValidation and UQ

SOS 10 March 6-9, 2006

Informatics Drivers

• Scale– Huge amounts of data– Visualization on multiple scales– Streaming data – “online” processing

• Presentation of Information– Making it meaningful

• Implementation– Code complexity– Architectures

• Quality– Representation of data– Dealing with model uncertainty– Dealing with missing data

SOS 10 March 6-9, 2006

Representing Data

• Challenge: Piecing the data together and extracting critical, relevant information in a timely manner

• Semantic Graphs or Attributed Relational Graphs (ARGs) are one way to integrate data from disparate sources

– Vertices represent people, places, locations, events, etc. – Edges represent the relationships between the vertices– ARG encodes web of relationships

• Graphs represent relationships and are the link between the model and processing

SOS 10 March 6-9, 2006

Motif Finding

Image Source:T. Coffman, S. Greenblatt, S. Marcus, Graph-based technologies for intelligence analysis, CACM, 47(3, March 2004): pp 45-47

SOS 10 March 6-9, 2006

One More Challenge

• Merging data with large-scale modeling and simulation– Informatics and modeling and simulation are not separate problems

• Example - Climate simulation– Climate predictions will drive economic decisions– Climate and economics will both drive behavior

Climatological feedback

SOS 10 March 6-9, 2006

Summary

• Scale will drive computing– Size of problem (in the traditional scientific computing model)– Amount of data

• Need to focus on how machines/simulation/information will be used– Presentation (visualization) of information– Support for design and decision making

• Software environments and complexity are limiting– Need a lightweight, simple environment that allows flexibility and linking of

components. (No problem)– Data representation is a key question. This will drive both software and

hardware design