neural nets for ground based gamma-ray astronomy g.m. maneva *, j.procureur **, p.p. temnikov * *...

Neural Nets for Ground Based Gamma-ray Astronomy

G.M. Maneva*, J.Procureur**, P.P. Temnikov* *Institute for Nuclear Research and Nuclear

EnergySofia, Bulgaria **Centre d'Etudes Nucleaires de Bordeaux-Gradignan,

France

INTRODUCTION

• In gamma ray astronomy in energy range from 10 GeV to 10 TeV the main kind of detectors use the atmosphere as a part of detector. Showers produced by primary particles consist from thousands of relativistic particles emitting Cherenkov radiation which forms a spot of blue light with a diameter about 200-300m and time duration about few nanoseconds

Gamma induced Cherenkov showers and imaging telescope

Imaging camera

Gamma induced Cherenkov showers and sampling detector

Progress

Difficulties of data analysis

• Several tenths or hundreds measured parameters

• Huge background of hadronic showers

( several order of magnitude more abundant)• Very unstable night light noise• Absence of calibration events require very

sophisticated and realistic Monte Carlo simulation of showers development and detector response

For high energy physisist

• Imagine that you have unbounded calorimeter (at least in transverse direction) with variable total absorption length (because primary interaction point is not fixed). Forget about calibration beams (primary energy is unknown).

• Try to identify very weak signal over huge background and find energy and incoming direction of primary particle.

If you don’t succeed in doing this we advice you to study the methods of

Artificial Neural Network (ANN)

ANN approach to the problem

• In the domain of classification problems ANN is an useful tool able to provide us a good test statistic t , performing mapping of the multidimensional feature space of the elementary events of both classes into one-dimensional function t, i.e.

• The mapping may be realized using non-linear function with many free internal parameters

• Traditionally this mapping is presented in the form of a network.

)(xtx

x

A simple form of ANN. Mode of learning: feed-forward and back propagation

x3

x2

x1

y2

y1

t

})({ ijki k

jkij vvxwfwft

Where f is the nonlinear activation function,usually of the form of

tanh(x)

or

1/(exp(-2x)+1).

And the matrix of weights w contents the parameters to be fitted to the data

MINUIT users

• Try to find the minimum of the function depending on several thousands free parameters

• No success : Study new methods of learning from data with

Artificial Neural Networks

We have applied the ANN methods for the discrimination of the gamma induced Cherenkov air showers, observed by the wave front sampling experiment CELESTE The detector (still in development) consists of 38 mirrors of 54 m2 reflecting the light to the top of a tour, where secondary optics, photomultipliers and electronics register the arrival times and amplitudes of the Cherenkov photons.

The data are collected in the typical for ground based gamma astronomy ON-OFF mode.

ON - the detector observes the source during a certain time ( about 20 minutes).

OFF - the detector follows the same trajectory in the absence of the source.

OFF is supposed to be equal to the background of ON.

But …it is far from the reality.

So, we faced a “simple” problem:

having ~20 000 OFF-events (in the 76-dimensional space) and the same quantity of ON-events (thought to be the same as OFF-background + γ-ray signal) to identify the practically undistinguishable set of γ-ray induced showers.

Here we resorted to ANN’s help.

ANN architecture

Error function to be minimized is

where N is the number of all training patterns, o i

and ti are the teaching value and the output for the i-th pattern.

Target (teaching) values : -0.8 (gamma), 0.8 (background) Training patterns used : 9000 OFF and 9000

Monte Carlo simulated gamma showers. Testing patterns : 1500 MC gamma + 1500 (+ 9000) OFF events.

)(2

1

1i

N

ii to

N

ANN output for two classes of events

Artificial ON (artON) As a Useful Tool for Ann-properties Investigation

ArtOn is an artificially created ON of 18000 showers, consisted in real OFF events + 1% of MC gamma. To study the ANN properties we examine the pair OFF-artON.

Typical behavior of training and testing errors with the epochs

Conventional approachOne chooses some stop epoch in the region of the broad minimum to interrupt the training. This choice is rather subjective because it leads to different values of physically interesting quantities (efficiency and rejecting power)

Our approachWe consider all the nets created in the minimum test region as equally representative (i.e. providing different but equally good mapping xt(x) )

Dependence of physical parameters on the epoch number

A reasonable way to treat the results in figure is to consider the range of variation of ε, pOFF and C on the domain of ERF- minimum as “systematic errors” intrinsic for the ANN - method. Such un approach avoids the subjectivity of the stop -epoch choice which leads to great scattering of the results, obtained with the same method.   Here is the efficiency of γ-identification, (fraction of γ with t<t0);

 pOFF is the probability of misidentification of a

background event as a signal, i.e. the fraction of OFF-events, declared as γ;pON: the same for the ON-events

C = (pON – pOFF)/ ( - pOFF) fraction of γ in ON-set

(for artON the real value is 0.01)

ON events as training background

patterns

In the case of a feeble signal it is possible to use a set containing the signal as

training background

ON may be used as a teaching background, without any

significant distortion of the results

The results for artificial ON as a training set

In both cases C is 0.01 with 25% systematic error

Quality factor used in the experiment Q = ε / pOFF

Usual experimental selection cuts yield Q=1.6ANN resultfor decision point t0=0 : Q=3.5for decision point t0= -0.6 : Q=4.7

Different impurity in training background set

Conclusions

• It is shown that in the case of weak signal the experimental data set (background + signal) can be used as a background training set

• It is argued that to reduce the uncertainty of physical parameters it is important to average them over the whole region of the minimum of network test error

Conclusion

Artificial Neural Network methods have not reached the state of

Artificial Intellect

but their applying requires some kind of

Art