# Presentation: 709352

## AISR PI Meeting 2008:  MTool

***Jet Propulsion Laboratory, California Institute of Technology***

***AISR PI Meeting 2008*****:*****  MTool***

***Martin.Lo @ jpl.nasa.gov,  ******5/7/2008***

*Streamlines for Titan Winds*

## MTool’s 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**

## SMD’s 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.**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## IDEA: Use Invariant Manifolds to Organize Data

**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**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Previous Work on Coherent Structures

**Finite Time Lyapunov Exponent Methods (Froschl****é, 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]**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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***

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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 R&TD 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**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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)**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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)**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Titan Wind Streamline Snapshot

**Wind Data provided by F. Oyafuo**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Titan Wind Streamline

**Titan Wind Streamline**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Descoped Task Breakdown

## 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**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## BACKUP CHARTS FOLLOW

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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**

## 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]**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## 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](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](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/](http://ddg.cs.columbia.edu/)**_
**Discrete Differential Complex, Discrete Elasticity Complex**
**	**_**[http://www.ima.umn.edu/~arnold/papers/icm2002.pdf](http://www.ima.umn.edu/~arnold/papers/icm2002.pdf)**_
**Homology computation tool: CHOMP: **_**[http://www.math.gatech.edu/~chomp/](http://www.math.gatech.edu/~chomp/)**_
**Lagrange Coherent Structure Tutorial and MANGEN software:**
**	**_**[http://www.cds.caltech/~shawn/LCS-tutorial/](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](http://www.msri.org/calendar/programs/ProgramInfo/243/show_program)**_
**Topological data analysis and visualization course: **_**[http://graphics.idav.ucdavis.edu/~vijayn/courses/MorseTheory/](http://graphics.idav.ucdavis.edu/~vijayn/courses/MorseTheory/)**_
**Pascucci, V., Robust Topology-Based Analysis of Large Scale Data, SC06 Conference, Tampa, FL, Nov. 2006**
**	**_**[http://www.pascucci.org/pdf-presentations/SC06-presentation.pdf](http://www.pascucci.org/pdf-presentations/SC06-presentation.pdf)**_

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## References

**Koon, Lo, Marsden, Ross [2000]: Chaos Journal 10(2), pp. 427- 469. ****	**_**[http://](http://www.gg.caltech.edu/~mwl)**__**[www.gg.caltech.edu/~mwl](http://www.gg.caltech.edu/~mwl)**_
**Shadden: ****	**_**[http://](http://www.cds.caltech/~shawn/LCS-tutorial/)**__**[www.cds.caltech/~shawn/LCS](http://www.cds.caltech/~shawn/LCS-tutorial/)**__**[-tutorial/](http://www.cds.caltech/~shawn/LCS-tutorial/)**_
**Couliette, Lekien: **_**[http://](http://www.cds.caltech/~shawn/LCS-tutorial/)**__**[www.cds.caltech/~shawn/LCS](http://www.cds.caltech/~shawn/LCS-tutorial/)**__**[-tutorial/](http://www.cds.caltech/~shawn/LCS-tutorial/)**_
**Elcott [07]: ****	**_**[http://www.geometry.caltech.edu/pubs/ETKSD07.pdf](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/ACYD05.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, 499–507, 2006.**
**[Waleffe]: Phys. Fluids, 15, 1517–1534, 2003.**
**	****	**
**	**

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology

## Responds to NASA’s Strategic Subgoal 3A

***“******Study planet Earth from space to advance scientific understanding and meet societal needs.”***

**Notes:**
The Fundamental Problem of Transport in the Solar System

1. What is the problem of transport in the Solar System?

2.  Why is this problem “fundamental” ? Why is this so important? What is the significance of this problem ?
This is a critical “foundational” problem underlying several fundamental scientific and engineering questions with critidcal impact on the development of space. 

3. Why study the dynamics of the Solar System when your main goal is to develop space, to enable new missions?

4. A Leverage Technology