Jens Zimmermann, Forschungszentrum Jülich, ACAT 021 Class Separation and Parameter Estimation with Neural Nets for the XEUS Project Jens Zimmermann [email protected]

Jens Zimmermann, Forschungszentrum Jülich, ACAT 02 1

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

Jens [email protected]

Max-Planck-Institut für Physik, München

MPI Halbleiterlabor, München

Forschungszentrum Jülich GmbH

The XEUS Satellite

Photon Recognition

Position and Charge Estimation

Conclusion


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


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


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 XMMOnboard 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)


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


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


Photon Recognition - Setup

4 inputs: 2×2 array normalized to maximum -mirrored to fix position of maximum charge

28 hidden neurons1 output: one photon (1.0) vs. two photons (0.0)

twophotons

onephoton

sim

ple

algo

rithm


Photon Recognition - Results

one photon

two photons

log

N (

%)

log

N (

%)

NN output

Training samples

Validation samples

Simple algorithm

Simple algorithm with patterns and energy cut is ``state of the art´´


Position Estimation (One Photon) - Setup

9 inputs: 3×3 array normalized to maximum -maximum charge centered

8 hidden neurons1 output: x-coordinate (normalized to 75µm)


Position Estimation (One Photon) - Results

Δx = xOUTPUT - xTRUE

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.

i

ii

m

mxx

µm75ˆ1


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 neurons2 outputs: x- and y-coordinate of left photon

(normalized to 4*75µm)


Position Estimation (Two Photons) - Results

x-coordinate y-coordinateσ = 9.6 µm σ = 14.1 µm

Difference is due to division into left and right photon in the training process

Δx = xOUTPUT - xTRUE Δy = yOUTPUT - yTRUE

% %

µm300ˆ1


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 neurons1 output: distance of the two incident positions

(normalized to 3*75µm)

d = sqrt[ (Δx)² + (Δy)² ]

mm


Distance Estimation (Two Photons) - Results

σ = 15.3 µm

Δd = dOUTPUT - dTRUE

%

µm225ˆ1


Outlook: Charge Estimation (Two Photons)

16+1 inputs20 hidden neurons1 output: charge of the left photon

σ = 683e

Setup:

Result without

preselection:

Result withpreselection:

Δc = cOUTPUT - cTRUE

σ = 323e


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


pn-CCD Simulation in Detail

drifttime4)tD=f(z, V)diffusion4)s=f(tD,T)

add signalto pixels5)Si,j=f(,x,y)i=x-1...x+1

morephotons?(pile-up)

get X-rayenergy E1)

interactiondepth

z = f(E)2)

withinsensitive3)volume?

escape photonP=f(E,z)

fano noisef(E)

getposition

x,y

no yes

add noisesCTI and

electronic

The figure shows the flow of an event simulation. Die-style boxes represent where random quantities are introduced.Optional effects are:

1) simulation includes radioactive sources (single or multiline) and continous (white or power law) spectra2) Interaction depth can reflect front and back illumination3) includes deadlayer absorption and non-interacting photons4) temperature dependent5) charge is contained within 3 3 pixels for pixel sizes > 50 µm

Simulated spectra have shown very good agreement with measurements.Nevertheless, additional effects and features to be taken into account include:

separate noise contributions (current leakage, read-out electronics etc.)individual pixel and channel properties (noisy, cold, hot, gain)common modeelectrostatic repulsion of signal chargesrealistic (gradient) dead layer modelparticle background (MIPS)

Data output(signal matrix)

Documents

Jens Zimmermann, Forschungszentrum Jülich, ACAT 021 Class Separation and Parameter Estimation with Neural Nets for the XEUS Project Jens Zimmermann [email protected]