![Page 1: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/1.jpg)
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
![Page 2: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/2.jpg)
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
![Page 3: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/3.jpg)
Gamma induced Cherenkov showers and imaging telescope
![Page 4: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/4.jpg)
Imaging camera
![Page 5: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/5.jpg)
Gamma induced Cherenkov showers and sampling detector
![Page 6: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/6.jpg)
Progress
![Page 7: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/7.jpg)
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
![Page 8: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/8.jpg)
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.
![Page 9: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/9.jpg)
If you don’t succeed in doing this we advice you to study the methods of
Artificial Neural Network (ANN)
![Page 10: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/10.jpg)
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
![Page 11: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/11.jpg)
A simple form of ANN. Mode of learning: feed-forward and back propagation
x3
x2
x1
y2
y1
t
})({ ijki k
jkij vvxwfwft
![Page 12: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/12.jpg)
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
![Page 13: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/13.jpg)
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
![Page 14: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/14.jpg)
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.
![Page 15: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/15.jpg)
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.
![Page 16: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/16.jpg)
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.
![Page 17: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/17.jpg)
ANN architecture
![Page 18: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/18.jpg)
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
![Page 19: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/19.jpg)
ANN output for two classes of events
![Page 20: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/20.jpg)
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.
![Page 21: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/21.jpg)
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) )
![Page 22: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/22.jpg)
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)
![Page 23: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/23.jpg)
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
![Page 24: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/24.jpg)
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
![Page 25: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/25.jpg)
Different impurity in training background set
![Page 26: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/26.jpg)
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
![Page 27: Neural Nets for Ground Based Gamma-ray Astronomy G.M. Maneva *, J.Procureur **, P.P. Temnikov * * Institute for Nuclear Research and Nuclear EnergySofia,](https://reader033.vdocument.in/reader033/viewer/2022051516/56649d605503460f94a40845/html5/thumbnails/27.jpg)
Conclusion
Artificial Neural Network methods have not reached the state of
Artificial Intellect
but their applying requires some kind of
Art