On the use of Graph Search Techniques for the Analysis of Extreme-scale Combustion Simulation Data

Janine Bennett1

William McLendon III1

Guarav Bansal2

Peer-Timo Bremer3

Jacqueline Chen1

Hemanth Kolla1

1Sandia National Laboratories, 2Intel, 3Lawrence Livermore National Laboratory

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Approved for Unlimited Unclassified Release, SAND # 2012-9242 C

HPC resources generate large, complex, multivariate data sets

Details: Lifted Ethylene Jet– 1.3 billion grid points– 22 chemical species, vector, & particle data– 7.5 million cpu hours on 30,000 processors– 112,500 time steps (data stored every 375th)– 240 TB of raw field data + 50 TB particle data

Recent data sets generated by S3D, developed at the Combustion Research Facility, Sandia National Laboratories

Efficiently characterizing & tracking intermittent features defined by multiple variables poses significant research challenges!

Our contribution: a framework for characterizing complex events in large-scale multivariate data

• Introduce attributed relational graphs (ARGs) as an efficient encoding scheme for relationships between spatial features – Defined by multiple variables – Spanning an arbitrary number of time steps– Representation achieves drastic data reductions

• Provide a mechanism for querying ARGs – Identify events conditioned on a variety of metrics

• Demonstrate results on large-scale combustion simulation data

Related work

Topology: Segment domain into features according to function behavior Level-set behavior: Reeb graph, contour tree, and variants

[Carr et al. 2003, Pascucci et al. 2007, Mascarenhas et al 2006, van Krevald et al 2004]

Gradient behavior: Morse and Morse-Smale Complex [Edelsbrunner 2003, Gyulassy et al 2007, 2008, Gunther et al 2011]

Multivariate feature analysis: Many correlation-based feature definitions[Gosink et al 2007, Chen et al 2011, Jaenicke et al 2007, Sauber et al 2006, Schneider et al 2008, Bennett et al 2011]

Feature tracking graphs: Capture spatial-temporal relationships [Edelsbrunner et al 2004, Bremer et al 2010, Muelder et al 2009, Widanagamaachchi et al 2012]

Graph search algorithms: Identify patterns in large-scale graphs[Barret et al 2007, Berry et al 2007, Gregor et al 2005, Siek et al 2002]

MTGL

What is an attributed relational graph (ARG)?

• ARG nodes correspond to spatial features– Each ARG node encodes

• Feature type• Time step• Optional per feature statistics

• ARG edges encode relationship between features– Spatial overlap metric – Supports feature tracking over time

ARG Nodes: Segment domain into relevant features

• Many options for segmenting the domain into features• Often features of interest are defined by a threshold around minima or maxima

of a particular variable

x

yf

ARG Nodes: Merge trees encode features of interest defined by a single variable for a range of thresholds

x

yf

Tree encodes behavior as sweep of function values is performed from maximum to minimum of range of interest

ARG Nodes: Merge trees encode features of interest defined by a single variable for a range of thresholds

x

yf

Tree encodes behavior as sweep of function values is performed from maximum to minimum of range of interest

ARG Nodes: Merge trees encode features of interest defined by a single variable for a range of thresholds

x

yf

Tree encodes behavior as sweep of function values is performed from maximum to minimum of range of interest

ARG Nodes: Merge trees encode features of interest defined by a single variable for a range of thresholds

x

yf

Tree encodes behavior as sweep of function values is performed from maximum to minimum of range of interest

ARG Nodes: Merge trees encode features of interest defined by a single variable for a range of thresholds

x

yf

Tree encodes behavior as sweep of function values is performed from maximum to minimum of range of interest

ARG Nodes: Merge trees encode features of interest defined by a single variable for a range of thresholds

x

yf

Tree encodes behavior as sweep of function values is performed from maximum to minimum of range of interest

ARG Nodes: Refine the tree to increase granularity of possible segmentations

x

yf

ARG Nodes: Features are defined as all sub-trees above a user-specified threshold

x

yf

x

yf

x

yf

ARG Edges: An overlap-based metric is used to encode feature behavior over time

t = 1

t = 2

t = 3

t = 4

t = 1

t = 2

t = 3

t = 4

ARG Edges: The same metric is used to encode relationships between different types of features

t = 1

t = 2

t = 3

t = 4

ARG Edges: Relationships can span multiple time steps

ARG Edges: Edge labels indicate degree of overlap between associated features

25 11

multi-way co-occurrence

Once the ARG is constructed, we can search for patterns of interest

co-occurrence time-lag features

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

• MTGL: Multi-Threaded Graph Library– Open source software– https://software.sandia.gov/trac/mtgl

• Given ARG and template– Filter: Remove all edges in ARG that cannot belong to template– Match: Find all possible template matches in filtered ARG

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template patternTemplate walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Searches are performed using a two-phase subgraph isomorphism heuristic: filtering & matching

ARG

Template walk

Case study: identification of deflagration fronts in HCCI combustion data

• Turbulent auto-ignitive mixture of Di-Methyl Ether under homogeneous charge compression ignition (HCCI) conditions

• Deflagration fronts: spatially collocated extrema of chemical reaction rates and diffusive fluxes

Reaction rate of OH Diffusion of OH

Feature family

Structure geometries

Hierarchy &statistics

temperature 4.0 GB 319 MBdiffusion OH 3.6 GB 11 MB

reaction rate OH 4.3 GB 534 MB

• Raw output data size: 78.2 GB (grid size = 560 x 560 x 560)– 703 MB/variable * 6 variables for 19 time steps

• Meta-data: computed in parallel on ORNL’s Lens system– 3 feature families:

• Each encoding size, minimum, maximum, mean, and variance of 6 different variables

• Data dependent costs O(minutes) per time step– Structure geometries only needed for ARG

construction (not queries)– Size of ARG: 504 KB

• Under 1GB required for fully flexible exploration and search on commodity hardware– O(seconds) for searches

Case study: ARG representation encodes complex relationships very compactly

template

connected components

14 6 2

nodes 487 310 352

edges 909 620 1005

Case study: Searching the ARG

A subset of the deflagration fronts identified

A subset of the full ARG (full size is 6563 nodes and 8903 edges)

Conclusion & future work

• Introduced attributed relational graphs (ARGs) as an efficient encoding scheme for relationships between spatial features

• Provided a mechanism for querying ARGs • Demonstrated results on large-scale combustion simulation data• Some domain knowledge required to construct ARG

– Which variables define features of interest– Range of potential time-lags between features

• Opportunities for future work– GUI tool for specifying search template patterns

• Leveraging per-feature statistics in queries– Linked views of ARG, search results, domain visualization– Dynamic ARGs

• Don’t require feature thresholds to be specified in advance• Instead these are runtime parameters to be explored

Questions?

Janine Bennett jcbenne@sandia.gov

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.