Siddharth Manay Chandrika Kamath Center for Applied Scientific Computing 2 March 2005

1. Siddharth ManayChandrika KamathCenter for Applied Scientific Computing2 March 2005 Progress Report on Data Analysis Work at LLNL: Aug’04 - Feb’05 UCRL-PRES-209947-DRAFT This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. http://www.llnl.gov/casc/sapphire/

2. Our progress on earlier applications • Feature selection for EHOs (data from DIII-D) • IDL code + instructions transferred to Keith@GAT • visit to GAT + talk • interest in licensing Sapphire software • sample scenario ready for the web • Separation of signals in climate data • a standalone C++ code available which uses our libraries for PCA/ICA • to be used in illustrating creation of workflows • sample scenario ready for the web Work done by Erick Cantu-Paz, Imola K. Fodor, Abel Gezahegne, Nu Ai Tang

3. New application: tracking in NSTX data • Joint work with PPPL (Klasky) • Problem: track the plasma over time • IDL code implementing a variant of block matching is too slow • Prototyping other block-matching approaches National Spherical Torus Experiment Leveraging LDRD funding (CK); work done by Erick Cantu-Paz, Cyrus Harrison

4. New application: classification of puncture (Poincaré) plots for NCSX • Joint work with PPPL (Klasky, Pomphrey, Monticello) • Classify each of the nodes: quasiperiodic, islands, separatrix • Connections between the nodes • Want accurate and robust classification, valid when few points in each node National Compact Stellarator Experiment Quasiperiodic Islands Separatrix

5. Piecewise Polynomial Models for Classification of Puncture Plots

6. Polar Coordinates • Transform the (x,y) data to Polar coordinates (r,). • Advantages of polar coordinates: • Radial exaggeration reveals some features that are hard to see otherwise. • Automatically restricts analysis to radial band with data, ignoring inside and outside. • Easy to handle rotational invariance.

7. Piecewise Polynomial Fitting: Dividing data into intervals. • Use the q-histograms to find intervals. • Need to divide the q domain into intervals that are: • Restricted to regions of q that have data. • Small enough so that polynomial will fit the data. • Large enough to span gaps where data is missing

8. Piecewise Polynomial Fitting: Computing polynomials • In each interval, compute the polynomial coefficients to fit 1 polynomial to the data. • If the error is high, split the data into an upper and lower group. Fit 2 polynomials to the data, one to each group. Blue: data.Red: polynomials. Black: interval boundaries.

9. Classification • The number of polynomials needed to fit the data and the number of gaps gives the information needed to classify the node: 2 Polynomials 2 Gaps  Islands 2 Polynomials 0 Gaps  Separatrix

10. Results 3995 points, Separatrix 250 points, 3 Islands Puncture 1, node 79 Zoom around =1.6 Zoom around =1.6

11. Future work • Set up web pages for climate and fusion scenarios • NSTX data: continue building and testing block-matching algorithms • NCSX data • continue interactions with Neil, Don, Scott • continue to refine and validate approach • investigate ways of making it more robust • investigate exploiting nearby nodes • design and implement in C++ for insertion into PPPL analysis pipeline