Class Separation and Parameter Estimation with Neural Nets for the XEUS Project

1. Class Separation and Parameter Estimation with Neural Netsfor the XEUS Project Max-Planck-Institut für Physik, München MPI Halbleiterlabor, München Forschungszentrum Jülich GmbH Jens Zimmermann zimmerm@mppmu.mpg.de The XEUS Satellite Photon Recognition Position and Charge Estimation Conclusion Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

2. X-Ray Satellite Missions • X-Ray Sources: • Hot plasmas (black body radiation and bremsstrahlung) • Highly relativistic electrons in magnetic fields • inverse Compton effect • X-ray observations tell about the hot universe and nuclear energy processes. Launched 1999 Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

3. XEUS: The X-Ray Evolving Universe Spectroscopy Mission XEUS will tell about • First massive black holes • First galaxy groups and their evolution into the massive clusters observed today • Evolution of heavy element abundances • Intergalactic medium using absorption line spectroscopy. Launch >2012 Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

4. XEUS - Datareduction and Trigger Onboard • Wide-Field-Imager: 1000×1000 pixeldetector (XMM: 384×400) • 16 bit/pixel, 1 ms/frame => 2 GB/s • Mirrors produce 200 times larger photonratethan on XMM Onboard data-reduction essential • Multiple-Readout for better energy resolution possible in DEPFET pixeldetectors • Which pixel should be read out more than one time? Trigger necessary Solution:Neural Hardware(Network implemented in FPGA device) :128 × 64 × 4 calculated within 400 ns(Jean-Christophe Prevotet) Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

5. Training Data from CCD-Simulation Simulation developed by Peter Holl, MPI Semiconductor Lab max. xx keV due to transparency of silicon for high energies • Training samples: • Photon energy spectrum • 37459 single photons • 37654 double photons • 8566 easily separable • 29088 ``pileups´´ • Crosses mark incident positions • In addition to photon energies always noise in pixels • Threshold value applied to find lit pixels Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

6. Network Training • C++ Code in ROOT framework (René Brun, Fons Rademakers) • based on NN-Code from J.P. Ernenwein, Université de Haute Alsace • modified by Ch. Kiesling, MPI Munich • Feed-Forward-Net • Three layers • Trained by backpropagation algorithm • Training results evaluated by Training/Validation-Comparison • ROOT TTree-structure used for general purpose training • Learning Parameters dynamically changed during training: • Reduce learning and momentum parameter by factor of 2when training error increased over the last two steps • Overtraining warning when training error decreasedwhile validation error increased successively two times Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

7. Photon Recognition - Setup two photons one photon simple algorithm 4 inputs: 2×2 array normalized to maximum - mirrored to fix position of maximum charge 28 hidden neurons 1 output: one photon (1.0) vs. two photons (0.0) Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

8. Photon Recognition - Results Simple algorithm with patterns and energy cut is ``state of the art´´ log N (%) one photon Training samples Validation samples two photons log N (%) Simple algorithm NN output Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

9. Position Estimation (One Photon) - Setup 9 inputs: 3×3 array normalized to maximum - maximum charge centered 8 hidden neurons 1 output: x-coordinate (normalized to 75µm) Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

10. Position Estimation (One Photon) - Results Center Of Mass method: Correction table filled by calculating COM-result for simulated events. COM: σ = 9.5 µm CCOM: σ = 5.2 µm NN: σ = 4.6 µm Δx = xOUTPUT - xTRUE Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

11. Position Estimation (Two Photons) - Setup 16+1 inputs: 4×4 array normalized to maximum, aligned to left and bottom, plus scale factor (maximum) 35 hidden neurons 2 outputs: x- and y-coordinate of left photon (normalized to 4*75µm) Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

12. Position Estimation (Two Photons) - Results % % Δx = xOUTPUT - xTRUE Δy = yOUTPUT - yTRUE x-coordinate y-coordinate σ = 9.6 µm σ = 14.1 µm Difference is due to division into left and right photon in the training process Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

13. Distance Estimation (Two Photons) - Setup d = sqrt[ (Δx)² + (Δy)² ] mm 16+1 inputs: 4 × 4 array normalized to maximum, aligned to left and bottom, plus one scale factor 22 hidden neurons 1 output: distance of the two incident positions (normalized to 3*75µm) Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

14. Distance Estimation (Two Photons) - Results % σ = 15.3 µm Δd = dOUTPUT - dTRUE Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

15. Outlook: Charge Estimation (Two Photons) 16+1 inputs 20 hidden neurons 1 output: charge of the left photon Setup: Result without preselection: σ = 683e σ = 323e Result withpreselection: Δc = cOUTPUT - cTRUE Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

16. Conclusion • Neural Networks are fast enough to performonboard trigger and data-reduction tasks • We developed a ROOT-based general purposeneural net framework • Neural Networks very efficient in photon recognition • Neural Networks 10% better in position estimationthan corrected center of mass method • Work in progress: • Getting information from pileup-events (Normally thrown away) • Study experimental data Jens Zimmermann, Forschungszentrum Jülich, ACAT 02

17. pn-CCD Simulation in Detail Jens Zimmermann, Forschungszentrum Jülich, ACAT 02