Machine learning technique to improve anti-neutrino detection efficiency for the ISMRAN experiment
PPrepared for submission to JINST
Machine learning technique to improve anti-neutrinodetection efficiency for the ISMRAN experiment
D. Mulmule, a , b , P. K. Netrakanti, a L. M. Pant a , b and B. K. Nayak a , b a Nuclear Physics Division, Bhabha Atomic Research Centre,Trombay, Mumbai, India - 400085 b Homi Bhabha National Institute,Anushakti Nagar, Mumbai, India - 400094
E-mail: [email protected]
Abstract: The Indian Scintillator Matrix for Reactor Anti-Neutrino detection - ISMRAN exper-iment aims to detect electron anti-neutrinos ( ν e ) emitted from a reactor via inverse beta decayreaction (IBD). The setup, consisting of 1 ton segmented Gadolinium foil wrapped plastic scintil-lator array, is planned for remote reactor monitoring and sterile neutrino search. The detection ofprompt positron and delayed neutron from IBD will provide the signature of ν e event in ISMRAN.The number of segments with energy deposit (N bars ) and sum total of these deposited energiesare used as discriminants for identifying prompt positron event and delayed neutron capture event.However, a simple cut based selection of above variables leads to a low ν e signal detection efficiencydue to overlapping region of N bars and sum energy for the prompt and delayed events. Multivariateanalysis (MVA) tools, employing variables suitably tuned for discrimination, can be useful in suchscenarios. In this work we report the results from an application of artificial neural network -the multilayer perceptron (MLP), particularly the Bayesian extension - MLPBNN, to the simulatedsignal and background events in ISMRAN. The results from application of MLP to classify promptpositron events from delayed neutron capture events on Hydrogen, Gadolinium nuclei and alsofrom the typical reactor γ -ray and fast neutron backgrounds is reported. An enhanced efficiency of ∼
91% with a background rejection of ∼
73% for prompt selection and an efficiency of ∼
89% witha background rejection of ∼
71% for the delayed capture event, is achieved using the MLPBNNclassifier for the ISMRAN experiment. Corresponding author. a r X i v : . [ phy s i c s . d a t a - a n ] M a y ontents In recent years, the measurement of reactor based anti-neutrinos ( ν e ) has provided key aspects inunderstanding the nature of neutrino interactions and their oscillations. Results from experimentssuch as Double Chooz, Daya Bay and RENO collaborations have reported measurements of θ mixing parameter [1–3] and possibility of searches for light sterile neutrinos [4]. Also an excess ofevents, in energy region ∼ ν e inducedinverse beta decays (IBD), has opened up new avenues for further studies in reactor based ν e [5–7].Various experiments, using moderate scale (few tonnes) detector, are being proposed or takingdata at very short baselines to further understand the properties associated with the reactor anti-neutrinos [8–11]. The Indian Scintillator Matrix for Reactor Anti-Neutrinos (ISMRAN) experimentis one such detector consisting of plastic scintillator (PS) bars in an array forming an active detectionvolume of 1.0 ton by weight [12]. ISMRAN is proposed to measure reactor ν e s for non-intrusivemonitoring of reactor along with the possibility of very short baseline oscillation searches of ν e tosterile states.ISMRAN is an above ground experiment comprising of 100 PS bars arranged in segmentedgeometry, each of dimension 100cm × × O ) coated aluminized mylar foils (areal density of Gd O : 4 . / cm ) and directlycoupled to a 3” PMT at both ends. A 10 cm thick lead (Pb) and 10 cm thick borated polyethylene(BP) shielding will enclose the full setup along with the use of muon veto scintillators on all sidesoutside the shielding structure. The location of ISMRAN is at a distance of ∼
13m from a 100MW th Dhruva reactor [14] core on a trolley based structure for allowing movement of the detectorto various distances from the reactor core. A schematic of complete ISMRAN setup is shown in– 1 –
Figure 1 . Schematic diagram of ISMRAN detector, 100 PS bars, inside a shielding of 10 cm of lead and 10cm of borated polyethylene on a mobile trolley. Outside the shielding structure are the muon veto scintillatordetectors.
Fig. 1. A high sampling rate (500 MS/s) digitizer based DAQ has been chosen for recording theoutput signals from the 200 PMT channels and the acquisition will be performed with minimumthresholds for offline event reconstruction. The complete detector system will be housed insidereactor hall and would face a harsh environment of reactor related backgrounds.The rate of interaction of reactor ν e per second ( N ν e ) inside the 1m scintillator volume of theISMRAN detector can be estimated using the below formula:N ν e = N p · P th · η · σ IBD π D · E f · . · − , (1)where the inputs are, N p : number of quasi-free protons in the scintillator volume, P th : thermalpower of the reactor in MW, η : detection efficiency, D : distance (in cm) between the detector andcenter of the core (assuming a compact core), E f : average energy released per fission in MeV and σ IBD = ∫ σ ( E ν e ) f ( E ν e ) dN ν e ( E ν e ) : the cross section (in cm ) of IBD averaged over the ν e spectrum(E ν e is the ν e energy and f ( E ν e ) is the ν e spectrum per fission). Using this formula the signal ratefor ISMRAN at 25% efficiency comes out to ∼ ν e events/day [12].Feasibility studies using simulations have been performed to evaluate the possibilities for ν e detection in ISMRAN setup for the choice of the detector configuration [15]. The sensitivity ofthe chosen setup is extensively studied for the sterile neutrino oscillation search [16]. It has been– 2 –alculated that for ISMRAN, a sterile neutrino sensitivity at 90% C.L. exclusion limits can beachieved with a moderate detection efficiency of 25% and energy resolution ( σ / E ) ∼ (cid:112) ( E ) .Improvements in detection efficiency and energy resolution, would help in increasing the sensitivityby almost ∼ ∼
25% would allow to distinguish ν e signal from background at 3 σ level in ∼
15 days of ISMRAN reactor ON data, where the backgroundrate of ∼ bars ) and their sum energy is performed. The prompt and delayedevents are further classified from simulated background events consisting of γ -rays and fast neutronfrom the surroundings in reactor hall. We also add a new variable D k , apart from the usual sumenergy and N bars , which improves the efficiencies of prompt and delayed events in terms of MLPclassification. Furthermore, the backgrounds due to cosmic muons and their induced neutrons,long-lived radioactive nuclei, especially Li / He, can mimic a signature of either prompt, delayedor both of IBD candidate events in ν e detection experiments [13]. Training and development ofMLP classifier for such background classification from the true IBD ν e events can be explored infuture work. Detection of ν e s from nuclear reactor is primarily done using the IBD reaction which has a ν e energy threshold of 1.806 MeV. In this reaction an ν e interacts with a proton in the detector volume(usually a scintillator) and produces positron and neutron (eq. 1). Due to the reaction kinematics,the positron carries majority of ν e energy. The positron deposits energy in the scintillator bars, viaionization, followed by production of two γ -rays of 0.511 MeV each, from its annihilation with anelectron. These γ -rays then deposit their energy in scintillator bars through Compton scattering.The energy deposited by positron and the resulting annihilation γ -rays forms the prompt event inISMRAN detector. While, the neutron having few keVs of energy undergoes thermalization in thedetector volume and gets captured on either Gd or H nuclei. The capture of neutron on H willproduce a mono-energetic γ -ray of 2.2 MeV as shown in equation 2. On the other hand, the neutroncapture on Gd leads to an emission of cascades of γ -rays, as shown in equations 3 and 4, and formsthe signature of delayed event. ν e + p → e + + n . (1)The capture cross-sections ( σ n − capture ) of thermal neutrons on Gd (eq. 3) and
Gd (eq. 4) are61000 b and 254000 b, respectively. These cross-sections are about 10 times higher than thatfor H nuclei. Therefore, after thermalization, the neutron produced from IBD interaction hashigher probability to get captured on the wrapped Gd foil outside plastic scintillator bar, than inthe hydrogenous bulk of the scintillator in ISMRAN geometry. In recent years, a great amountof experimental and theoretical work is done in understanding and improving the modeling ofthe de-excitation of Gd nucleus and emission of γ -ray cascades particularly in context of IBD– 3 –vents [17–19]. n + p → d ∗ → γ, E γ = . , σ n − capture = . , (2)n + Gd → Gd ∗ → γ (cid:48) s , (cid:213) E γ = . , σ n − capture = , (3)n + Gd → Gd ∗ → γ (cid:48) s , (cid:213) E γ = . , σ n − capture = . (4)The thermalization and capture of neutron produced from IBD happens after a mean time delay,ranging from a few µ s up to an order of a few 100 µ s, from the time of positron event dependingon the capture agent position and its concentration in the detector volume. Electron anti-neutrinoevents in ISMRAN are therefore identified through the detection of these prompt and delayed eventpairs separated in time. The ISMRAN detector, positioned at ∼
13 m from the natural uranium fuel core inside the reactorhall, is a first attempt of its kind for detection of reactor ν e in extreme conditions of background.Inside reactor hall, the ambient γ -ray and neutron background, are expected to be of the order of ∼ Hz with 100 PS bars [12]. The low IBD cross-section of ν e and relatively higher backgroundrates inside reactor hall poses a challenging task of online triggering of the prompt or delayed events.To minimize the losses in triggering of the IBD events, the online data is timestamped and essentiallycollected in a triggerless mode for all the plastic scintillator bars. The offline analysis consists ofevent building by grouping of the PS bars (N bars ) hit according to the stored timestamps and obtainthe sum energy deposition by adding the individual energy deposited in each PS bar. After eventbuilding, a classification of an event as either prompt-like or delayed-like needs to be done forfurther assigning it as a signature of an ν e candidate event. At this stage, the information aboutthe mean time delay between an identified prompt-like and delayed-like event may be added as avariable to classify ν e candidate event pairs from other background pairs. Usually, this classificationof prompt-like and delayed-like events can be achieved with a selection cut on the sum energy andN bars variables. However, there is a significant overlap between the individual variable distributionsin these event classes which results in reduction of overall ν e detection efficiency. To understand the IBD event characteristics and the corresponding signal detection efficiencies inISMRAN, monte-carlo based IBD events are generated using GEANT4 [20] (version 4.10.4). Thephysics processes listed in QGSP_BIC_HP are used along with the inclusion of photon evaporationmodel for the de-excitation of Gadolinium nucleus and the resulting γ -ray cascades. The simulationsare performed using the parameterization of ν e spectrum from ref [21], the cross section calculationsfrom ref [22, 23] and the fission fractions for different isotopes from ref [24]. The sum energyand N bars variables are separately recorded for the prompt and delayed events for each simulatedIBD interaction in ISMRAN. Only PS bars with deposited energy above the threshold: E Thbar = 0.2MeV are considered due to the minimum operating threshold of the signal in the real experiment.Figure 2 (a) shows the sum energy and 2(b) the N bars distributions with threshold condition for– 4 – / N d N / d E IBD
Prompt Delayed (a) bars
Bar Multiplicity (N00.10.20.30.40.5 ba r s ( / N ) d N / d N IBD
Prompt Delayed (b)
Figure 2 . Panel (a) Sum Energy and (b) N bars distributions for prompt and delayed events obtained fromGeant4 simulation for IBD events in ISMRAN. both prompt and delayed events. As previously discussed, the overlap in both the distributions forprompt and delayed events is evident in these distributions. An attempt may be made to keep theprompt and delayed event domains exclusive of each other and achieve event classification usingthe criteria: N promptbars = delayedbars > =
4, on delayed eventselection. The ν e signal detection efficiencies obtained for such a simple cut based selection of theprompt and delayed events based on sum energy and N bars are shown in table 1, using the ISMRANsimulated IBD events [12]. A significant loss in ν e detection efficiency is observed for this cutbased classification. Moreover, even with these stringent cuts the classification of events as promptor delayed is still ambiguous. PANDA experimental setup, using an array of 100 plastic scintillatorbars have reported detection efficiency of 11.6% from simulations [11]. Table 1 . ν e detection efficiency with cuts on prompt and delayed events.Loose cuts Efficiency (%) Stringent cuts Efficiency (%)1.8 < E prompt (MeV) < promptbars = 2 or 3 69 2.2 < E prompt (MeV) < promptbars = 2 or 3 670.8 < E delayed (MeV) < delayedbars > = < E delayed (MeV) < delayedbars > = < E prompt (MeV) < promptbars = 2 or 30.8 < E delayed (MeV) < delayedbars > = < E prompt (MeV) < promptbars = 2 or 33.0 < E delayed (MeV) < delayedbars > = To obtain higher ν e detection efficiencies by using the sum energy and N bars variables, oneneeds to relax the selection criteria on these variables. This may lead to increase in the false promptor delayed event rate contribution, from natural backgrounds ( K and
Tl), fast neutrons andthose from the ambient γ -ray activity mostly coming from the neutron captures on the material– 5 –n the vicinity of the detection setup in reactor hall. By performing multivariate analyses (MVA),using the sum energy and N bars variables, one can enhance the discrimination of the prompt eventsfrom the above mentioned backgrounds improving the ν e detection efficiency. The event classifiersused in this approach can either be based on multivariate statistics or pattern recognition algorithms.Furthermore, it is possible to utilize additional variables, formed using a weighted combination ofbase variables, tuned for better discrimination and achieving better signal detection efficiency andpurity. Assessment of energy resolution of prompt events from such a classifier will be consideredin future studies where a detailed measurement and identification of different sources of the realisticbackground rates in the reactor hall are available. Data analysis techniques have evolved extensively in the current phase of high energy physics withpowerful techniques available to efficiently extract signal information in background dominateddata sample. Techniques using multivariate statistics or machine learning algorithms, such asMaximum Likelihood [25, 26], Fischer discriminant [27], Boosted Decision Trees [28] or MultilayerPerceptron (MLP) [29, 30], to separate signal from background events have already been successfullyimplemented to obtain various interesting physics results. In this work we are going to focus on theuse of artificial neural networks (ANN), especially, MLP for the classification of prompt positronsignature as signal event against delayed neutron capture and reactor γ -ray background events. Themultilayer perceptron (MLP), is the traditional form of artificial neutral network [31]. It is a machinelearning algorithm with a structure consisting of an input layer, one or more hidden layers, andan output layer. The MLP algorithm basically approximates a function mapping an n -dimensionalinput x to a m -dimensional output f in the real number space. The MLP layers are fully connectedi.e. the output of each node is the weighted sum of the outputs of all nodes in the previous layer plusa bias term. These inputs are operated upon by a non-linear sigmoid function like tanh at each nodeof a hidden layer [30]. Under certain assumptions, an MLP architecture with a single hidden layercan be shown to approximate any function to arbitrary precision given a sufficient number of hiddennodes [32, 33]. A supervised learning method [34] is traditionally used to determine the weightsand biases used in an MLP. During this phase, the MLP is presented with data samples whereboth x and the corresponding output, f , referred to as the ground truth, are known, for e.g. fromsimulations. The measure of the error between the output of the MLP and the ground truth, referredto as the ‘loss’, is computed. An algorithm called the back-propagation algorithm [35] calculates thegradient of this loss as a function of the weights and biases, which is then minimized by altering theweights and biases using the stochastic gradient descent method [36]. Repeated application of theabove procedure is carried out till the errors are reduced to an acceptable level. However, in orderto reduce the number of iterations to cut down on the computation time an alternative approachcalled the Broyden-Fletcher-Goldfarb-Shannon (BFGS) method can be utilized while adapting thesynapse weights [37]. This method uses the second derivatives of the error function for adjustingthe weights in each iteration. In this paper, we present the results of prompt signal and delayedbackground classification for ISMRAN detector by using the ‘Bayesian’ extension of MLP withthe above BFGS method incorporated in it, referred to as - ‘MLPBNN’ in the ROOT TMVA [38]package. The MLPBNN approach allows for increasing the complexity (more hidden units and/or– 6 –ore layers) of the architecture while simultaneously employing a regulator to avoid over-training.This is achieved through addition of another term in the network error function that effectivelypenalizes large weights, consequently controlling the complexity of the model. For purposes ofbrevity in writing and also acknowledging the fact that MLPBNN is an extension of the morefundamental MLP algorithm, we will use only the term ‘MLP’ for the MLPBNN classifier hereonwards. Similar work adopting the convolution visual network from the machine learning methodsis used to describe neutrino interactions based on their topology [39]. The MVA based classification, presented in this work, uses a simulated sample of 5M IBD events inISMRAN detector. PS bars with energy deposit above the threshold : E
Thbar = . bars > ν e candidate event. The reconstructed positron prompt eventsfrom the N bars and sum energy deposition are defined as “Reco prompt” events. The neutron capturedelayed events on Gd comprises of ∼
75% of total neutron captures in ISMRAN detector [12] andthe remaining ∼
25% takes place on hydrogen nuclei in the bulk of the scintillator volume. All suchneutron capture delayed events which can be misidentified as prompt events are defined as “Falseprompt”. The choice of this terminology is made to stress the fact that, the emphasis is on accuratelyclassifying the prompt event, as it is crucial to derive the ν e energy distribution. The neutron captureevent on the other hand may not be specific to the IBD neutron event. A similar signature as anIBD delayed event is expected when a fast neutron produced from reactor surroundings entersISMRAN, thermalizes in PS bars and gets captured on Gd or H. A detailed measurement of fastneutron background in reactor hall is required to simulate such fast neutron background event rate inISMRAN and is not currently available. Hence, for this study, we are considering the simulated IBDneutron capture delayed events as background, since the final cascade γ -ray signature would be samein both the cases. Since, these fast neutron events will be uncorrelated to the reconstructed promptevent, the mean time delay variable will not be effective to discriminate such background pairsfrom the real IBD event pairs. For both methods 100000 events are used for the classifier training.Another set of 100000 events, completely different from the training set, are simultaneously usedfor testing and evaluation purposes. In the case of MLP, additional inputs such as neuron type, thenumber of hidden layers, number of neurons in a hidden layer, testing iterations and frequency ofthe tests are provided to the classifier. – 7 – .6 - - - ( / N ) d N / d R (a) Reco PromptFalse Prompt ( / N ) d N / d R Reco PromptFalse Prompt (b) F a l s e P r o m p t R e j e c t i on MVA Method :
MLPLikelihood (c)
Figure 3 . Panel (a) and (b) shows the comparison of performance for likelihood and MLP classifiers onsimulated IBD reco prompt and false prompt events in ISMRAN detector, respectively. Panel (c) shows thecomparison of ROC curve for the MLP and likelihood classifiers.
The classifier response (R) of likelihood and MLP methods are presented in Fig. 3 (a) and (b),respectively. The separation between the reco prompt and false prompt events for MLP is betterthan likelihood classifier. Figure 3 (c) shows the reco prompt efficiency vs false prompt rejectioncurve shows the ‘receiver operator characteristics’ - ROC for the two classifiers. A ROC curve canprovide an optimal working point in terms of true positive and false positive selection rates for anypredictive model, which could be applied to the data, chosen for classification of events. The ROCcurve shows better false prompt background rejection in case of MLP, even for higher reco promptefficiencies. These results make MLP classifier a better choice for ISMRAN IBD events out of thetwo compared classifier methods. It must be pointed out that the chosen MLP architecture in ourstudy uses two hidden layers. The first hidden layer uses N +5 nodes while the second one uses N nodes, where N corresponds to the number of input variables. One of the input node apart from theinput variables is the bias node, which is implicit in the MLP architecture. The two hidden layerconfiguration is found to have optimal performance for reasonable number of iterations in errorminimization leading to less computational time. MLP response for reco prompt and false prompt events for IBD interactions in ISMRAN
Thermal neutron capture on Gd nucleus is followed by emission of γ -ray cascades from its de-excitation. These cascades of γ -rays mostly span multiple PS bars and hence the average N bars insuch events would be higher than a mono energetic γ -ray emission by neutron capture on H nuclei.Also, the sum of these deposited energies in PS bars is expected to be around 8 MeV, for a fullycontained event. A selection cut on the MLP classifier, using only sum energy and N bars variable,which selects ∼
90% of reco prompt events from the sample can only provide ∼
65% rejection ofthe false prompt events, as shown in Fig. 3(c). Further improvements in the existing frameworkare therefore needed to increase the reco prompt efficiency of the classifier response. In order toachieve this, we introduce a new variable constructed using the weighted individual bar energydeposits formulated as: D k = ( E total ) − k × ( (cid:205) i ( w i × ( E i ) k )) , where E total is the total sum energy, E i is the individual PS bar energy deposit, k is a real number, and the weight factor is defined as– 8 – k D00.050.10.150.2 k ( / N ) d N / d D (a) Reco PromptFalse Prompt ( / N ) d N / d R Reco PromptFalse Prompt (b) F a l s e P r o m p t R e j e c t i on MVA Method : MLP k w D k w/o D (c) Figure 4 . Panel (a) shows the reco prompt and false prompt event separation for D k variable for IBD eventsin ISMRAN. Panel (b) shows the response after application of MLP classifier including the D k variable alongwith N bars and sum energy variable. Panel (c) shows the improvement in the ROC curve of MLP classifierwith inclusion of D k variable for reco prompt efficiency and false prompt rejection. w i = E i / E total . This additional variable is inspired by discrimination variables used in quark andgluon jet identification in high energy proton-proton collisions [40]. In case of D k , the choice ofexponent k as 2.5 is observed to provide better discrimination ability compared to other values ofk. The formulation of the variable D k is such that it makes use of the difference in the energydeposition profiles of the reco prompt events and false prompt events and consequently enhancestheir separation as seen in Fig. 4(a). Figure 4(b) shows better separation in the MLP classifierresponse, after inclusion of D k and Fig. 4(c) shows the comparison of ROC curves with and withoutinclusion of D k for reco prompt efficiency and false prompt rejection. It can be seen that thereis a significant improvement in false prompt rejection for a given reco prompt efficiency with theinclusion of D k in the MLP classifier. All the MLP classifier results presented, here onwards, arewith the inclusion of D k along with sum energy and N bars variables. MLP response for reco prompt events and false prompt events from neutron capture on Gdand H separately in ISMRAN
It is important to evaluate the MLP classifier response, separately, to the false prompt events ( / N ) d N / d R Gd (a) Reco PromptFalse Prompt ( / N ) d N / d R H (b) Reco PromptFalse Prompt F a l s e P r o m p t R e j e c t i on MVA Method : MLP
GdH (c)
Figure 5 . Panel (a) and (b) shows the MLP classifier response for reco prompt events from positron andfalse prompt events from neutron capture on Gd and H, respectively. Panel (c) shows the comparison of ROCcurve for the reco prompt efficiency and false prompt rejection from neutron capture events on Gd and H. – 9 –rom Gd and H capture delayed events and to obtain the corresponding rejection rates. This isrequired, because both nuclei undergo de-excitation process leading to different sum energy andN bars signatures. The motive behind studying classification performance for H capture events andcomparing it to Gd captures is to evaluate and ensure that the MLP framework performs equallyeffectively in both scenarios.This is addressed within the MLP framework by individually studyingthe false prompt events from neutron capture on Gd and H. Figure 5 (a) and (b) show the MLPresponse and classification between a reco prompt from positron and false prompt event for neutroncapture on Gd and H, respectively. The separation in the classifier response is good in both theevents from Gd and H capture events from the reco prompt events. Figure 5 (c) shows the falseprompt event rejection due to the Gd and H capture events as a function of reco prompt efficiencies.It can be seen that the rejection of false prompt events using MLP is quite effective in case of bothGd and H capture events keeping reasonable reco prompt efficiency.
MLP response for reco prompt events and reactor γ -ray background events in ISMRAN The experimental setup of ISMRAN detector inside reactor hall poses a hostile environment foranti-neutrino detection due to the ambient reactor γ -ray backgrounds. These γ -rays are emanatingmostly from the neutron capture on the surrounding materials present in the reactor hall, namely thestainless steel structures and beam dumps used in reactor operations or for various neutron scatteringexperiments. We have taken a reference γ -ray spectrum for such events from the PROSPECTexperimental site selection studies [41], particularly at the NBSR site where the γ -ray activity isquite intense and varied in energy. This allows for the test of the MLP classifier response in amore realistic reactor γ -ray background. The above reactor background γ -ray distribution is usedas an input in our GEANT4 simulations and events are recorded for a shielded ISMRAN detectorgeometry. These events are considered as the background events, and the MLP classificationis trained for discriminating the reco prompt events. The reco prompt event and reactor γ -raybackground event separation are shown in the Fig. 6(a) along with the ROC curve in Fig. 6(b). Areco prompt efficiency of ∼
90% is achieved with ∼
70% of reactor related γ -ray background eventrejection. MLP response for reco prompt events and fast neutron background events in ISMRAN ( / N ) d N / d R Reco Prompt g Reactor (a) R e j e c t i on g R ea c t o r MVA Method :
MLP (b)
Figure 6 . Panel (a) MLP classifier response for reco prompt events from positron and reactor γ -raybackgrounds. Panel (b) ROC curve for the reco prompt efficiency and reactor γ -ray background rejection. – 10 – ( / N ) d N / d R Reco PromptFast Neutron (a) F a s t N eu t r on R e j e c t i on MVA Method :
MLP (b)
Figure 7 . Panel (a) MLP classifier response for reco prompt events from positron and proton recoil eventsfrom fast neutrons. Panel (b) ROC curve for the reco prompt efficiency and fast neutron rejection.
A fast neutron, produced either from cosmogenic source, muon spallation from shielding material orfrom reactor background, can enter ISMRAN detector and produce an event where a large fractionof neutron energy is transferred to a proton inside the PS bar. Such proton recoil events usually tendto have signatures very close to the reco prompt event from positron. To simulate such proton recoilevents a uniform distribution of fast neutrons from 2 MeV to 20 MeV were generated in GEANT4inside the ISMRAN setup. The sum energy deposition, N bars and D k variables from such protonrecoil events are then classified from the reco prompt events using MLP. Figure 7 (a) shows theMLP response of reco prompt events and proton recoil events from fast neutrons. The separationin terms of classifier response for these events is reasonably good. Figure 7 (b) shows the ROCcurve for the reco prompt efficiency and rejection of proton recoil events from fast neutron. A recoprompt efficiency of ∼
80% is achieved with a rejection of proton recoil events close to 84%.
Performance evaluation of MLP for reco prompt and delayed events in ISMRAN
To test the performance of MLP classifier, we prepare a sample of 100000 events of reco promptevents with a mixed sample of false prompt events from Gd and H neutron capture delayed events.The inclusion of H neutron capture events as potential delayed event is one of the advantages ofusing the MLP method over the cut based selection which rejected such events and led to reduced ν e signal detection efficiencies. The MLP performance parameters such as reco prompt efficiency,purity and their product are calculated as a function of different selection of cut values on the MLPresponse. Figure 8 shows the relative behavior of these three parameters for different selection cutson the MLP classifier in percentages. In the region of MLP response values from 0.2 to 0.6 theproduct of signal efficiency and purity is close to 70%. The performance of the MLP classifieris obtained in terms of figures of merit (FOM), s / (cid:112) ( s + b ) and s /√ b, where s and b define thereco prompt signal and false prompt background events, respectively, in the sample. The quantitys / (cid:112) ( s + b ) can be used to maximize the efficiency of the reco prompt signal events with the classifierresponse and s /√ b is used for obtaining the maximum purity of the reco prompt signal in presenceof false prompt background events. Similar analysis using MLP, is also performed for an IBDneutron capture delayed event under classification. Here, the false delayed events are those recoprompt events which may have similar signature of IBD neutron capture delayed events in terms of– 11 – P e r c en t age Reco Prompt efficiencypurityefficiency*purity
Figure 8 . Reco prompt efficiency, purity and product of efficiency and purity for MLP as a function ofdifferent selection cut values on the MLP output. sum energy deposition, N bars and D k variables. Figure 9 shows the efficiency, purity and productof efficiency and purity for the reco delayed events. The efficiency, purity and false rejection forreco prompt and delayed events obtained for specific cut values on MLP response are tabulated intable 2 and 3 respectively. These selection cut values are chosen, so as to maximize the s / (cid:112) ( s + b ) and s /√ b of both event classes and provide an evaluation of the MLP performance.The efficiency value, shown in table 2, of 91.5%, as obtained for maximally efficient classifi-cation of reco prompt events, is a significant gain over the earlier cut based efficiency of 69%(seetable 1). The maximum purity of the reco prompt events can reach ∼
93% at the MLP selection cutof 0.88 with an efficiency of ∼
56% for the reco prompt events. The optimal selection of cut value P e r c en t age Reco Delay efficiencypurityefficiency*purity
Figure 9 . Reco delay efficiency, purity and product of efficiency and purity for MLP as a function of differentselection cut values on the MLP output. – 12 – able 2 . Efficiency, purity and false rejection performance for reco prompt events.MLP cut value Efficiency (%) Purity (%) False Rejection (%)s /√ s + b 0.37 91.5 77.3 73.1s /√ b 0.88 56.4 93.5 96.1 Table 3 . Efficiency, purity and false rejection performance for reco delayed events.MLP cut value Efficiency (%) Purity (%) False Rejection (%)s /√ s + b 0.37 88.7 80.5 71.3s /√ b 0.70 66.9 92.3 94.4 on the MLP response may be selected in these ranges to achieve a moderate reco prompt signalefficiency with a reasonable reco prompt signal purity. Similarly, table 3 presents the maximumpossible reco delayed event efficiency of 88.7% obtained at a cut of 0.37, with a purity of 80.5% andfalse rejection of 71.3%. For the selection of s /√ b, a optimal cut of 0.70, selects the reco delayedevents with 92.3% purity with a false delayed rejection of 94.4%. The achieved efficiency, purityand false rejection obtained from MLP classifier for reco prompt and reco delayed events are thepreliminary estimations and provides a better performance than the results obtained from a simplecut based analysis. The final ν e energy spectra is closely related to the measured reco prompt energydistribution. To evaluate the spectral shape, the performance of the MLP classifier on selecting thereco prompt signal events is tested using 100000 independent IBD events. All the events whichsatisfies the classifier cut selection above 0.37 are chosen as reco prompt signal events. Figure 10(a) shows the prompt sum energy distribution of input events (shown in black), after application ofthe MLP classifier response on the reco prompt events (shown in red dashed) and that from a simplecut based analysis choosing ‘loose’ cuts on reco prompt events, as in table 1(shown in dashed dotblue). It can be seen that using MLP a significant improvement in the efficiency and spectral shapeof prompt energy distribution is obtained as compared to a simple cut based analysis results. Avery conservative systematic uncertainty is evaluated due to the MLP response variations. Thesource of these systematic uncertainties arise primarily from the choice of input model used fortraining and testing of the MLP classifier, incorporation of all the associated backgrounds in thereactor hall and due to the variation in the efficiencies of the detector over the entire data takingduration. We varied the MLP response cut value by 5% and estimated the uncertainty of 2.4 % inthe reco prompt energy distribution. Figure 10 (b) shows the false prompt energy distribution forMLP and cut based analysis which are filtered as reco prompt signal events. It can be seen thatthe MLP based classifier are accepting less number of false prompt events which can be markedas reco prompt signal events as compared to that from a cut based analysis. Also more number ofbackground events, at around 2MeV from neutron capture on H, are misidentified as reco promptsignal events in case of cut based analysis as compared with MLP classifier. Overall the purity ofthe reco prompt signal events is higher in case of MLP classifier as compared to a simple cut basedanalysis. – 13 – N o r m a li z ed C oun t s Prompt
TrueMLP (Reco)Cuts (Reco) (a) N o r m a li z ed C oun t s Prompt
MLP (False)Cuts (False) (b)
Figure 10 . Panel(a) : Prompt sum energy distribution for true input, reco prompt events classified with MLPand from a cut based analysis. Panel(b) shows the false prompt events which are misidentified as reco promptevents using MLP classifier and cut based analysis.
Machine learning technique using multilayer perceptron algorithm is applied to discriminate recoprompt events arising from IBD interactions from the false prompt events from different sourcesof background in the ISMRAN detector. Using simulations, it has been shown that this techniqueprovides an excellent separation of reco prompt events from false prompt events which are fromthe delayed neutron capture on Gd, H, fast neutron and γ -rays background from reactor. Theperformance of MLP classifier is better as compared to the statistical methods of cut based orlikelihood based classification. An addition of new variable, D k , obtained from weighted energydeposits in bars further improves the response of MLP classifier. Prompt signal efficiencies closeto ∼
91% has been obtained while rejecting ∼
73% of the false prompt events in ISMRAN detector.In future, MLP classifier may be used to discriminate other source of backgrounds which includecosmogenic muon spallation and neutron induced backgrounds for obtaining better anti-neutrinodetection efficiency in ISMRAN.
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