1. Jens Zimmermann, Forschungszentrum Jülich, ACAT 021 Class Separation and Parameter Estimation with Neural Nets for the XEUS Project Jens Zimmermann zimmerm@mppmu.mpg.de Max-Planck-Institut für Physik, München MPI Halbleiterlabor, München Forschungszentrum Jülich GmbH The XEUS Satellite Photon Recognition Position and Charge Estimation Conclusion

2. Jens Zimmermann, Forschungszentrum Jülich, ACAT 022 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

3. Jens Zimmermann, Forschungszentrum Jülich, ACAT 023 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

4. Jens Zimmermann, Forschungszentrum Jülich, ACAT 024 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 photonrate than 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)

5. Jens Zimmermann, Forschungszentrum Jülich, ACAT 025 Training Data from CCD-Simulation Training samples: Photon energy spectrum 37459 single photons 37654 double photons 8566 easily separable 29088 ``pileups´´ Simulation developed by Peter Holl, MPI Semiconductor Lab Crosses mark incident positions In addition to photon energies always noise in pixels Threshold value applied to find lit pixels max. xx keV due to transparency of silicon for high energies

6. Jens Zimmermann, Forschungszentrum Jülich, ACAT 026 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 2 when training error increased over the last two steps Overtraining warning when training error decreased while validation error increased successively two times

7. Jens Zimmermann, Forschungszentrum Jülich, ACAT 027 Photon Recognition - Setup 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) two photons one photon simple algorithm

8. Jens Zimmermann, Forschungszentrum Jülich, ACAT 028 Photon Recognition - Results one photon two photons log N (%) NN output Training samples Validation samples Simple algorithm Simple algorithm with patterns and energy cut is ``state of the art´´

9. Jens Zimmermann, Forschungszentrum Jülich, ACAT 029 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)

10. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0210 Position Estimation (One Photon) - Results Δx = x OUTPUT - x TRUE COM: σ = 9.5 µm CCOM: σ = 5.2 µm NN: σ = 4.6 µm Center Of Mass method: Correction table filled by calculating COM-result for simulated events.

11. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0211 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)

12. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0212 Position Estimation (Two Photons) - Results x-coordinatey-coordinate σ = 9.6 µmσ = 14.1 µm Difference is due to division into left and right photon in the training process Δx = x OUTPUT - x TRUE Δy = y OUTPUT - y TRUE %

13. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0213 Distance Estimation (Two Photons) - Setup 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) d = sqrt[ (Δx)² + (Δy)² ] mm

14. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0214 Distance Estimation (Two Photons) - Results σ = 15.3 µm Δd = d OUTPUT - d TRUE %

15. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0215 Outlook: Charge Estimation (Two Photons) 16+1 inputs 20 hidden neurons 1 output: charge of the left photon σ = 683e Setup: Result without preselection: Result with preselection: Δc = c OUTPUT - c TRUE σ = 323e

16. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0216 Conclusion  Neural Networks are fast enough to perform onboard trigger and data-reduction tasks  We developed a ROOT-based general purpose neural net framework  Neural Networks very efficient in photon recognition  Neural Networks 10% better in position estimation than corrected center of mass method  Work in progress:  Getting information from pileup-events (Normally thrown away)  Study experimental data

17. Jens Zimmermann, Forschungszentrum Jülich, ACAT 0217 pn-CCD Simulation in Detail