Updated results from a new Neural

cartcletchAI and Robotics

Oct 19, 2013 (3 years and 7 months ago)

61 views

Updated results from a new Neural
Network tool:


e
-
/
p
-

獥灡牡瑩潮s

energy measurement from e.m. showers

E. Barbuto, C. Bozza, A. Cioffi,
M. Giorgini

OPERA Collaboration Meeting

Nagoya, Japan, 30 Jan


4 Feb 2004

Outline


Features of the Neural Network (NN) Software


MC simulation used for the training


Results on :


Particle (e
-
/
p
-
⤠獥灡牡瑩潮


Energy reconstruction in e.m. showers


Conclusions



Full generality/modularity



Platform and language independence (the library has
been tested and debugged both under Windows and Linux)



It can be used by any user program, even in server mode



Users can extend the library even without recompiling



GUI and console interface allowing an interactive
monitoring of the training and testing phases

Neural Network library structure

Multilayer Perceptron

:
several
layers of “neurons”, each one with
its transfer function

Network Type

(see C. Bozza, Gran Sasso Coll. Meeting, May `03)


Output layer

Hidden layer

Input layer

GEANT simulation of a complete OPERA brick (56 lead targets and
56 emulsion
-
base
-
emulsion sheets)

lead (1mm)


p

,e

x

y

z

MC simulation for training and test

First step : e/
p

摩獣物d楮i瑩渠潮汹⁴ r潵杨 瑨敩 浵汴楰汥m䍯C汯浢m
scattering before interacting/showering
(see E. Barbuto, Phys. Coord. July `03)

New step : algorithm taking into account the showers

Full analysis :
MCS of primary particle + shower analysis

..... 56

Shower analysis (MC data)

5 GeV e
-

5 GeV
p
-

10 GeV e
-

10 GeV
p
-

1 GeV e
-

1 GeV
p
-

Description of the shower analysis



Goals :


1.

electron/pion separation

2.

electron energy reconstruction


Requests for a good shower description :


Consider as much as possible tracks belonging to the shower


Do not integrate over background tracks


In order to achieve these requirements :

1.
we opened a
50 mrad

cone around the primary

2.
for each track, we required a maximum relative angle
of
400 mrad

with respect to the primary direction

3.
the tracking thresholds was set at
~
10 MeV

(due to the
tracking efficiency)

NN structure

INPUT LAYER : 672 NEURONS

Emulsion films crossed by primary particle before showering (1 var.)

Number of film where the cone starts (1 var.)

Number of charged particle detected per film inside the cone (112 var.)

x
-
coordinates sigma for charged particles in the cone (112 var.)

y
-
coordinates sigma for charged particles in the cone (112 var.)

x
-
angular sigma for charged particles in the cone (112 var.)

y
-
angular sigma for charged particles in the cone (112 var.)

Dq
砠批 䵵汴M灬攠p潵汯浢 卣慴瑥物湧n潦⁴o攠灲業慲y ⠵㔠癡v.)

Dq
y 批 䵵汴M灬攠p潵汯浢 卣慴瑥物湧n潦⁴o攠灲業慲y ⠵㔠癡v.)

㘷㌰〠⠶㜲砱〰⬱〰砱⤠(敩杨瑳

䡉䑄䕎⁌E奅Y 㨠㄰〠獩杭潩搠湥畲潮o

OUTPUT LAYER : 1 logistic neuron giving a
number between 0 and 1

Input variables

NN Output

NN

Training

A special feature : missing data


E (GeV)

n
film

28

n
film

72

n
film

108

1

67%

2%

0%

3

90%

88%

3%

5

95%

94%

18%

7

96%

96%

29%

9

97%

97%

35%

The decreasing of the primary particle energy leads to a higher number of missing input data

Real emulsion data come with inefficiencies (missing tracks in
one or more sheets)

Each missing track corresponds to some missing network inputs

In order to have a tool able to analyze real data, the situation of
missing data must be correctly handled

Example: percentage of events with a minimum number of films crossed by
particles of the shower

Electron ID: training the network


Training events: 2000 e
-

+ 2000
p
-

with a continuous energy spectrum [0
-
10] GeV


Weight updating every 10 events


90 epochs


Electron ID: test with variable energies

First test : MC data having a
continuous spectrum [0
-
10] GeV

Testing events:


5000

e
-

+ 2500
p
-

卥灡牡瑩潮o癡汵攠
x

]0;1[
:

if network output <
x



敬e捴c潮

if network output >
x



灩潮

x

= 0.9

Electrons

(5000 ev.)

Pions

(2500 ev.)

A suitable value could be
x
= 0.9


Electron ID: test on fixed energies

We tested the NN
also

with e
-
/
p
-

particles with fixed energies

3 GeV e
-

3 GeV
p
-

NN output

NN output

5 GeV e
-

5 GeV
p
-

NN output

NN output

e
-
/
p
-

獥灡牡瑩潮s敦晩捩敮捹

E (GeV)

f

ID(e
-
)

ID(
p
-
)

1

7
㜮㤥

㠱8㌥

9
㔮㠥

3

9
㠮㌥

9
㠮㌥

㤹9㤥

5

9
㤮㌥

9
㤮㌥

㄰〥

7

9


9
㤮㈥

9
㤮㠥

9

9


㤹9㜥

9


0
-
10

82%

83.3%

9
8.5%

ID(e
-
): fractions of electrons correctly identified

ID(
p
-
⤺⁦ 慣a楯湳i潦⁰o潮猠捯牲散e汹l楤敮i楦楥i

f

=
ID(e
-
)

䥄I
p
-


Energy reconstruction: variable e
-

energies


0
-

10 GeV electrons

Total entries : 5000

Mean Value :
-
0.012 RMS : 1.667

Fit Mean:
-
0.006 Sigma : 0.885


0
-
2 GeV electrons

Total entries : 1000

Mean Value :
-
0.787 RMS : 2.084

Fit Mean:
-
0.113 Sigma : 0.625

E
real
-
E
rec
(GeV)

E
real
-
E
rec
(GeV)

E
real
-
E
rec
(GeV)


8
-

10 GeV electrons

Total entries : 1000

Mean Value: 0.635 RMS: 1.366

Fit Mean : 0.322 Sigma: 0.664

Energy reconstruction: fixed e
-

energies


9 GeV electrons

Total entries : 5000

Mean Value : 8.347 RMS : 1.523

Mean Fit : 8.832 Sigma : 0.512


5 GeV electrons

Total entries : 5000

Mean Value : 4.990 RMS : 1.502

Mean Fit : 5.178 Sigma : 1.164


1 GeV electrons

Total entries : 5000

Mean Value : 1.773 RMS : 1.957

Mean Fit : 1.241 Sigma : 0.795


7 GeV electrons

Total entries : 5000

Mean Value : 6.953 RMS : 1.562

Mean Fit : 7.352 Sigma : 0.980

Erec(GeV)

Erec(GeV)

Erec(GeV)

Erec(GeV)

Energy reconstruction resolution


As already said, this NN can work with missing input data, so it was trained and tested with
ALL THE

EVENTS
, independently from the number of crossed layers or particle produced.

The reconstruction precision could be improved selecting data with a minimum number of emulsion

films crossed by charged particles in the selected cone (this is the usual procedure used in standard NN)

3 GeV electrons (all events)

Total entries : 5000

Mean Value : 2.978 RMS : 1.444

Mean Fit : 2.938 Sigma : 0.914

3 GeV electrons,


28 films


Total entries : 4532

Mean Value : 2.707 RMS : 0.699

Mean Fit: 2.720 Sigma : 0.631

Erec(GeV)

Erec(GeV)

D
E/E

31%

D
E/E

23%

Conclusions


A general neural network software has been developed


Special feature: deals with missing input data


It can be used in various modes and environments
(Windows/Linux, Interactive/Server)


Results:


(1) e
-
/
p
-

獥灡牡瑩潮 w楴i
f


>

98% for 3<E<10 GeV


(2) Electron momentum reconstruction can be done
without selecting the data (like in the real case!)