Genesis Orals template

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AISR PI Meeting 2008 MTool
Streamlines for Titan Winds
Martin.Lo _at_ jpl.nasa.gov, 5/7/2008
Jet Propulsion Laboratory, California Institute
of Technology
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MTools Interdisciplinary Collaboration

• Dr. Martin Lo, PI Section 388
• Unfunded (by MTool) Collaborators
• Dr. Amy Braverman Section 388
• Dr. Eric Fetzer Section 324
• Dr. Robert West Section 322
• Dr. James Friedsen Section 322
• Fabiano Oyafuso Section 388
• Dr. Paul von Allmen Section 388
• Prof. Alan Barr Caltech Graphics Group
• Prof. Mathieu Desbrun Caltech Applied Geometry
  Lab
• Prof. Kathleen Howell Purdue University,
  Aeronautics
• Dr. Rodney Anderson U. Colorado Boulder,
  Aeronautics
• Prof. Stan Osher UCLA, IPAM

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SMDs Information Big Bang

• Massive High Dimensional Data from Science
  Missions
• From Complex Coupled Nonlinear Dynamical Systems
• Examples
• Sun Spots Solar Wind Magnetosphere Earth
  Weather
• Ocean Atmosphere Climate
• MTool Multidimensional Manifold Data Analysis
  Tool
• Provides Dynamical Systems Approach to This
  Problem.

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IDEA Use Invariant Manifolds to Organize Data

• Use Invariant Manifolds to Organize Data Model
  Dynamics
• Manifolds Manifest as Spatio-Temporal Coherent
  Structures in Data
• Structures Provide Compact Low Dimensional
  Dynamical Map of Data
• Like Interplanetary Superhighway for Space
  Trajectories

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Previous Work on Coherent Structures

• Finite Time Lyapunov Exponent Methods (Froschlé,
  Wiggins, Haller, Jones, Marsden)
• Compute Periodic Orbits in Turbulent Flows
  (Kawahara, Waleff)

• Red Curve LCS
• Green Lobes
• LCS Recent Uses
• Design underwater gliders in Monterey Bay
• Study pollution in Florida coast
• Model Titan Atmosphere
• video S. Shadden, Caltech,
• MANGEN S/W Lekien, Couliette

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Explore New Computational Technologies

• New Computational Mathematical Methods
• Discrete Differential Geometry Discrete Extrior
  Calculus
• Computational Topology
• Numerical Manifold Embedding (Whitney,
  Nash-Moser)
• Integral Geometry (Generalized Tomographic
  Methods)
• Use computer graphics, vision, and image
  processing methods
• Already using many advanced mathematics from
  above
• Reconstruct Manifolds from Point Clouds
• Level Set Methods
• Curvature Flows

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Benefits to SMD Missions, NASA

• Introduce New Mathematical and Computational
  Methods to NASA Science and Instrument Community
• Provide Advanced Tools for
• Data Analysis, Modeling, Simulation
• Process, Analyze, and Visualize Massive High
  Dimensional Data
• Enable NASA to
• Design Build Better Instruments
• Design Fly New Mission Concepts
• Provide Tools to Help NASA Solve the Global
  Warming Problem

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FY08 Goals Demonstrate Approach

• Use LTool Concrete Use Case Methodology
• Help drive technology and software development
• Case 1 Simple Dynamical Systems
• Analytic Flows Double Gyre, ABC Flow
• Restricted 3 Body Problem
• Case 2 Global Wind Vector Field from Titan GCM
• Bob West et al., JPL RTD Strategic Initiative
  for a Titan GCM
• Case 3 Use AIRS MISR Data over Pacific Basin
• Amy Braverman, Eric Fetzer
• Case 4 Create New Image of ? Ray Sky from BATSE
  Data (GRO)
• James Ling, William Wheaton, Gary Case (LSU)
• New Spherical Radon Transform or Circular Radon
  Transform
• Best Effort Basis

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Extract Coherent Structures in Titan Winds

• Goals
• Visualize and identify coherent structures in 3D
  Titan winds
• Compare different Titan atmospheric models (JPL,
  Caltech)
• Algorithm
• Compute Lagrangian flow from simulated global
  wind data
• Compute finite time Lyapunov exponents (FTLE)
  from flow
• Segmentation of FTLE to identify time-varying
  invariant manifold boundaries, i.e. the coherent
  structures
• Challenges
• Solving Flow of ODE for sparse discrete vector
  field on sphere
• Solutions Embed ODE in 3-space (Barr),
  Spherical Harmonics B-spline
• Segmentation of fuzzy FTLE point set data
• Solutions (1) Voronoi-based surface
  reconstruction (Desbrun)
• (2) Level set method for surface
  reconstruction (Osher)

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Some Challenging Problems

• Solving Flow of ODE for sparse discrete vector
  field on sphere
• Solutions (1) Embed ODE in 3-space (Barr),
• (2) Spherical Harmonics B-spline
• Segmentation of fuzzy Finite Time Lyapunov
  Exponent point set data
• Solutions (1) Voronoi-based surface
  reconstruction (Desbrun)
• (2) Level set method for surface
  reconstruction (Osher)

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Titan Wind Streamline Snapshot
Wind Data provided by F. Oyafuo
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Titan Wind Streamline
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Budget Status

• Original Proposal 772K 3 Years
• Partial Funding 125K 1 Year
• Burdened Cost Plan 59,803 (Year to Date)
• Burdened Cost 41,995
• Variance 17,808
• Increase time commitment on project

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Descoped Task Breakdown
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Plans

• Computation of Coherent Structures
• AISR MISR data Over Pacific Ocean
• Titan Winds
• Complete Lagrangian flow computation of discrete
  vector fields on spheres and patches (2D and 3D)
• Simple Dynamical Models
• Kathie Howell at Purdue, Rodney Anderson at CU
  Boulder
• Level Set-Based Surface Reconstruction of Point
  Set
• Working with Stan Osher, UCLA,
• Voronoi-Based Surface Reconstruction of Point Set
• Working with Mathieu Desbrun, Caltech
• Propose Again to FY08 AISR Proposal

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BACKUP CHARTS FOLLOW
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Descoped Task Breakdown

• I. Task Management
• Implementation Plan
• User Reviews
• Final Review
• II. Research Algorithm Development
• Manifold Analysis
• Manifold Computation
• Multiresolution Irregular Grids
• Manifold Operations
• Discrete Differential Geometry
• Discrete Exterior Calculus
• Computational Homology
• Parallel Algorithms
• Manifold Analysis
• Discrete Differential Geometry
• Visualization

• III. Software Implementation
• Manifold Analysis Tool
• Discrete Differential Geometry Tool
• Interactive User Environment
• Parallel Computation Tool
• Visualization Tool
• NASA Data Interface Tool
• IV Final Delivery
• Test and Integration
• User's Guide
• Final Report
• Legend
• Text Color Eliminated Tasks
• Task descoped

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Discrete Exterior Calculus (DEC)

• Main Idea Represent solutions to differential
  equations as N-dimensional surfaces
• More compatible with measurements and data with
  noise
• Includes ODEs PDEs
• Easy Formulation
• Rapidly Developing Field

Elcott 05
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References

• de Silva, V., R. Ghrist, Homological Sensor
  Networks, Notices of the AMS Jan. 2007.
• DARPA Topological Sensor Program and Topological
  Data Analysis Program, 2006
• http//www.darpa.mil/DSO/thrust/math/math_fm.htm
• UNESCO GIS training on topological data
  structure, Topology and Spatial Relationships
  1999.
• http//ioc.unesco.org/oceanteacher/oceanteacher2/
  other/GISModules/module_g/module_g1.html
• Discrete Differential Geometry Forum (tutorials,
  links, papers, DEC) http//ddg.cs.columbia.edu/
• Discrete Differential Complex, Discrete
  Elasticity Complex
• http//www.ima.umn.edu/arnold/papers/icm2002.pdf
  
• Homology computation tool CHOMP
  http//www.math.gatech.edu/chomp/
• Lagrange Coherent Structure Tutorial and MANGEN
  software
• http//www.cds.caltech/shawn/LCS-tutorial/
• Georgiev, T., Vision, Healing Brush, and Fiber
  Bundles, Human Vision and Electronic Imaging X,
  San Jose, CA, March 18, 2005, pp. 293-305.
• MSRI Computational Applications of Algebraic
  Topology, Aug 14 Dec 15, 2006
• http//www.msri.org/calendar/programs/ProgramInfo
  /243/show_program
• Topological data analysis and visualization
  course http//graphics.idav.ucdavis.edu/vijayn/c
  ourses/MorseTheory/
• Pascucci, V., Robust Topology-Based Analysis of
  Large Scale Data, SC06 Conference, Tampa, FL,
  Nov. 2006
• http//www.pascucci.org/pdf-presentations/SC06-pr
  esentation.pdf

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References

• Koon, Lo, Marsden, Ross 2000 Chaos Journal
  10(2), pp. 427- 469. http//www.gg.caltech.edu/m
  wl
• Shadden http//www.cds.caltech/shawn/LCS-tutori
  al/
• Couliette, Lekien http//www.cds.caltech/shawn/L
  CS-tutorial/
• Elcott 07 http//www.geometry.caltech.edu/pubs
  /ETKSD07.pdf
• Elcott 05 http//www.geometry.caltech.edu/pubs
  /GSD05.pdf
• Li 06 http//ourocean.jpl.nasa.gov/publication
  /Ocean06-final.pdf
• http//ourocean.jpl.nasa.gov/
• Desbrun 99 http//www.geometry.caltech.edu/pubs/
  DMSB_SIG99.pdf
• Alliez http//www.geometry.caltech.edu/pubs/AC
  YD05.pdf
• Animation and artwork on Interlanetary
  Superhighway by Cici Koenig using MAYA.
• http//www.gg.caltech.edu/mwl
• wang Level Set Method for Solid Optimization,
  CAD/CG 2005 Tutorial, Hong Kong.
• Kawahara Nonlin. Processes Geophys., 13,
  499507, 2006.
• Waleffe Phys. Fluids, 15, 15171534, 2003.

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Responds to NASAs Strategic Subgoal 3A

• Study planet Earth from space to advance
  scientific understanding and meet societal
  needs.