Transcript Class Separation and Parameter Estimation with Neural Nets

Class Separation and Parameter Estimation with Neural Nets
for the XEUS Project
Jens Zimmermann
[email protected]
Max-Planck-Institut für Physik, München
MPI Halbleiterlabor, München
Forschungszentrum Jülich GmbH
The XEUS Satellite
Photon Recognition
Position and Charge Estimation
Conclusion
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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X-Ray Satellite Missions
 X-Ray Sources:
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Launched 1999
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.
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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XEUS: The X-Ray Evolving Universe Spectroscopy Mission
XEUS will tell about
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Launch >2012
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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.
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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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)
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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Training Data from CCD-Simulation
Simulation developed by Peter Holl, MPI Semiconductor Lab
Training samples:
• Photon energy spectrum
• 37459 single photons
• 37654 double photons
• 8566 easily separable
• 29088 ``pileups´´
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
max. energy
due to transparency
of silicon for high
energies
• Crosses mark
incident positions
• In addition to
photon energies
always noise in pixels
• Threshold value
applied to find lit
pixels
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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
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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two
photons
one
photon
simple algorithm
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)
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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log N (%)
Photon Recognition - Results
Simple algorithm with patterns and
energy cut is ``state of the art´´
one photon
Training samples
log N (%)
Validation samples
two photons
Simple algorithm
NN output
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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
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Position Estimation (One Photon) - Results
Center Of Mass method:
COM:
σ = 9.5 µm
xm

x
m
i
i
i
Correction table filled by
calculating COM-result
for simulated events.
CCOM:
σ = 5.2 µm
NN:
σ = 4.6 µm
Δx = xOUTPUT - xTRUE
1 ˆ 75µm
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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)
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Position Estimation (Two Photons) - Results
%
%
Δx = xOUTPUT - xTRUE
x-coordinate
σ = 9.6 µm
1 ˆ 300µm
Δy = yOUTPUT - yTRUE
y-coordinate
σ = 14.1 µm
Difference is due to division into left and right photon in the training process
Jens Zimmermann, Forschungszentrum Jülich, ACAT 02
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Distance Estimation (Two Photons) - Setup
d  (  x ) 2  ( y ) 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)
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Distance Estimation (Two Photons) - Results
%
σ = 15.3 µm
1 ˆ 225µm
Δd = dOUTPUT - dTRUE
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Outlook: Charge Estimation (Two Photons)
16+1 inputs
20 hidden neurons
1 output: charge of the left photon
Setup:
Result
without
preselection:
σ = 683e
Result with
preselection:
σ = 323e
Δc = cOUTPUT - cTRUE
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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
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pn-CCD Simulation in Detail
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