Synapse. A Neutron Spectrum Unfolding Code Based on Generalized Regression Artiﬁcial Neural Networks

In its broadest sense, the term artiﬁcial intelligence indicates the ability of an artifact to perform the same types of functions that characterize human thought. The goal of AI is to use algorithms, heuristics and methodologies based on the ways in which the human brain solves problems. Artiﬁcial neural networks recreate the structure of the human brain imitating the learning process. The Artiﬁcial neural networks theory has provided an alternative to classical computing for those problems in which traditional methods have delivered results that are not very convincing or not very convenient such as in the case of the neutron spectrometry and dosimetry problem for radiation protection purposes, using the Bonner spheres spectrometer as measurement system, mainly because many problems are encountered when trying to determine the neutron energy spectrum of a measured data. The most delicate part of the spectrometry based on this system is the unfolding process, for which several neutron spectrum unfolding codes have being developed. However, these codes require an initial guess spectrum in order to initiate the unfolding process. Their poor availability and their not easy management for the end user are other associated problems. Artiﬁcial Intelligence technology, is an alternative technique that is gaining popularity among researchers in neutron spectrometry research area, since it o ﬀ ers better results compared with the traditional solution methods. In this work, "Synapse", a neutron spectrum unfolding code based on Generalized Regression Artiﬁcial Neural Networks technology is presented. The Synapse code is capable to unfold the neutron spectrum and to calculate 15 dosimetric quantities using the count rates, coming from a BSS as the only entrance information. The results obtained show that the Synapse code, based on GRANN technology, is a promising and innovative technological alternative for solving the neutron spectrometry and dosimetry problems.


Artificial intelligence and neural networks
Learning and intelligence are intimately related to each other [1]. Learning is an inherent feature of human being and intelligence could be defined by its intrinsic properties such as the ability to deal with new situations, to solve problems, to answer questions, to create plans, etc., [2].
Machines were constructed in order to provide a means for humans to operate and achieve certain tasks, or to replace the human effort in its entirety [3].
The principles of learning can be applied to machines to improve their performance, and is one of the newest fields in research, innovation and technological development known as Artificial Intelligence (AI) [4,5], which is part of the new information and communication technologies of the fourth industrial revolution known as Industry 4.0.
AI seeks to understand intelligent entities and must be able to store knowledge, to apply the stored knowledge in problem solving and to acquire new knowledge through experience [1].
The goal of AI is to use algorithms, heuristics and methodologies based on the ways in which the human brain solves problems [2,3].
In the last decades, several technological trends have been created for the development of systems based on AI such as Expert Systems (ES) [6], Fuzzy Logic (FL) [7], Genetic Algorithms (GA) [8], Artificial Neural Networks (ANNs) [9], among others.
Recently, ANN are receiving more attention as a connectionist approach for building intelligent machines with structured models [9].
The central connectionist principle is that mental phenomena can be described by interconnected networks of simple and uniform units [10].
Units are to a connectionist model what neurons are to a biological neural network. It is important to mention that most of connectionist models are computer simulations executed on digital computers [11].
The learning ability of a neural network is achieved through applying a learning or training algorithm [12]. Training algorithms are mainly classified into three groups: supervised, unsupervised and reinforcement learning.
# Please ensure that you use the most up to date class file, available from EAI at http://doc.eai.eu/publications/transactions/ latex/ * Corresponding author. Email: morvymm@yahoo.com.mx The ANNs theory has provided an alternative to classical computing for those problems in which traditional methods have delivered results that are not very convincing or not very convenient.
Neutron spectrometry and dosimetry for radiation protection purposes, using the Bonner Spheres Spectrometer (BSS) as the measurement system, is other research area if interest [21,22].

Neutron spectrometry with artificial neural networks
Neutrons are produced by different ways and can be found in nature or produced artificially [23]. In general, neutrons are more difficult to detect than gamma rays because of their weak interaction with matter and their large dynamic range in energy, extending from few thousandths of eV to several hundreds of MeV [24].
Also, they are in a broad variety of energy distributions, named neutron-fluence spectrum or simply neutron spectrum [25].
Because neutrons have mass but no electrical charge, they cannot directly produce ionization in a detector, and therefore, cannot be directly detected [26]. This means that neutron detectors must rely upon a conversion process where an incident neutron interacts with a nucleus to produce a secondary charged particle [26,27]. These charged particles are then directly detected, and from them, the presence of neutrons is deduced [26][27][28][29][30].
Spectral information must generally be obtained from passive detectors which respond to different ranges of neutron energies such as the multi spheres Bonner system or Bonner spheres system (BSS) [31], which has been used to unfold the neutron spectrum because it has an almost isotropic response, can cover the energy range from thermal to GeV neutrons, and is easy to operate [32]. However, the weight, time consuming procedure, the need to use an unfolding procedure and the low resolution spectrum are some of the BSS drawbacks [33][34][35].
The measurement of the energy distribution of the intensity of a neutron radiation field is very important for radiation protection purposes, however, the derivation of the spectral information is not simple mainly because the unknown neutron spectrum is not given directly as a result of the measurements [33][34][35].
If a sphere d has a response function R d (E), and is exposed in a neutron field with spectral fluence θ E (E), the sphere reading M d is obtained by folding R d (E) with θ E (E), this means to solve the Fredholm integral equation of the first kind shown in equation 1, [ This folding process takes place in the sphere itself during the measurement. Although the real θ E (E) and R d (E) are continuous functions of neutron energy, they cannot be described by analytical functions, and, as a consequence, a discretised numerical form is used as is showed in equation 2: where C j is j th detector's count rate; R i , j is the j th detector's response to neutrons at the i th energy interval; θ i is the neutron fluence within the i th energy interval and m is the number of spheres utilized.
The dose is also important mainly due it is the variation of the intensity of neutron radiation as a function of angle of incidence on a body situated in the radiation field, however, the determination of neutron dose in nuclear facilities, generally requires to know the neutron energy spectrum incident on the body [23][24][25][26][27][28][29][30].
To unfold the neutron spectrum, θ, several methods have been used and during the last years, attempts have been made to develop new neutron spectrum unfolding codes, however, some drawbacks of these codes are: require an "initial spectrum", i.e., the spectrum that results from the unfolding process depends on how similar the initial spectrum is of the spectrum that is being sough, the management is not easy for the end user and their poor availability.
One more drawback is the computation of the neutron detectors response matrices, which is not a trivial task, since each value of the response matrix must be calculated individually using Monte Carlo simulations. The calculation of these values is also affected by multiple factors, which generate considerable error values.
At the time of writing this research work, only the information published by the International Atomic Energy Agency (IAEA) [67], is available in the form of a compendium of neutron spectra. This is a collection of a set of neutron spectra calculated in very different experimental places and conditions that would be very difficult to build by ourselves.
The compendium contains a large collection of detector responses and neutron spectrum such as neutron spectrum of isotopic neutron sources, nuclear reactors, accelerators for medical use, reactors for research in physics, cosmic rays, etc.
Also contains the BSS response of neutron detectors based on 6 LiI(Eu) and 3 He, as well as the fluence to dose conversion coefficients for 15 dosimetric quantities and several survey instrument meters which, as before mentioned, calculating each value is very complex.
Among researchers, AI technology has been proposed as an alternative approach for solving the drawbacks associated to the neutron spectrum unfolding problem and is gaining popularity since it offers better results compared with the traditional solution methods [43][44][45][46][47].
In neutron spectrometry, the theory of ANN has offered a promising alternative to the classic calculations made with traditional approaches. Previous researches indicate that Feed Forward Backpropagation Neural Networks (FFBPNN) perform well and this kind of network has been the most popular approach used in this research area [48][49][50][51][52][53][54].
In preliminary works, FFBPNN were used to solve the neutron spectrum unfolding problem. Although the results have been encouraging, the more serious drawback of FFBPNN is the learning and architectural parameter optimization as well as the large amount of time inverted just to determine these parameters [48][49][50][51][52][53][54].
Despite FFBPNN are very flexible, their process is highly parallel and can be used to solve diverse problems [55,56], the structural and learning parameters of the network must be set before any training can begin and there are no clear rules how to set them although the optimal selection of these parameters, determine the success of the training.
The estimation of the structural and learning parameters are often determined using the trial-anderror technique, that produces networks with poor performance and generalization capabilities, which affect its application in real problems.
Another drawbacks of FFBPNN are: the training can require a substantial amount of time to gradually approach good values of the weights.
The size of the training data has to be very large and often it is almost impossible to provide enough training samples as in the case of the neutron spectrometry problem.
Adding new information requires retraining the network and this is computationally very expensive [57,58].
Due to the aforementioned problems, alternatives were sought to solve the associated drawbacks of FFBPNN. An alternative was to use Generalized Regression Artificial Neural Networks (GRANN), which 3 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 falls into the category of Probabilistic Neural Networks (PNN) a subclass of Statistical Neural Networks (SNN) [59][60][61].
GRANNs have been successfully applied in other optimization and classification problems. Due to the intrinsic nature of this kind of network, is capable to solve the parameter optimization problems of FFBPNN architectures, since only one parameter is required to be optimized.
The learning of FFBPNN can be described as trial and error while GRANN use a statistical approach in their prediction algorithm, which is capable of working with only few training samples. Unlike FFBPNN, GRANN use a statistical approach in their prediction algorithm which is based on the Bayes strategy for pattern recognition [59][60][61]. In this sense, the experience is learned not by trial but by experience others made for the neural network.
Opposite to FFBPNN, GRANN are very flexible and new information can be added immediately with almost no retraining. The biggest advantage is the fact that the probabilistic approach of GRANN works with one-steponly learning and uses a single common radial basis function kernel bandwidth, σ , that is tuned to achieve an optimal ANN learning [59][60][61].
In addition to the above mentioned, the time required for training GRANNs, is significantly reduced from hours to milliseconds, compared to the FFBPNNs training process, since only one iteration is required to train GRANNs.
In preliminary works, FFBPNN and GRANN were trained and tested and the performance of both architectures was compared in the solution of the neutron spectrun unfolding problem. The results obtained showed that GRANNs solve the parameter optimization problems of FFBPNN, have a better performance and solve the neutron spectrum unfolding problem with greater efficiency.
However, scientific and technological tools have not been developed that allow applying this type of technology with efficiency in real experimental places [64,65].
In consequence, scientific computational tools are needed in order to train, to test, to analyze, and to validate GRANN technology in this research domain and to use it in real experimental places.
In collaboration agreement with the OMADS company, an enterprise dedicated to the research, innovation and technological development [66], the aim of this research work was to study, to analyze, to design and to implement Synapse, a neutron spectrum unfolding code based on GRANN technology, which is capable to unfold the neutron spectrum and to calculate 15 different dosimetric quantities using the count rates, coming from a BSS, as the only entrance information.
The code solves the neutron spectrometry and dosimetry problems with high performance and generalization capacity. The results obtained show that the Synapse code is a promising alternative which can be used for solving the neutron spectromtery and dosimetry problems and can be applied in real experimental places.

Generalized regression artificial neural networks
GRANN is a type of supervised Feed Forward Neural Network (FFNN) introduced by Donald F. Specht in 1991 [62]. Opposite to FFBPNN, where data may be propagated forward and backward many times until an acceptable error is found, the training of GRANN is very fast because the training data set propagates forward only once [59][60][61][62][63].
The structure of the calculations for the probabilistic density function in GRANN has striking similarities to FFBPNN, however, inside the neurons, GRANN use functions based on knowledge resulting from the Bayes strategy for pattern classification. The strength of a GRANN lies in the function that is used inside the neuron. The regression performed by GRANN is given by eq. 4: For a non-parametric estimate of f (x, y), one consistent estimator is the Gaussian function which is a good choice for estimating the probability density function, f . The probability estimatorf (x, y) is based on sample values x i and y i of the random variables X and Y given by eq. 5: Were p is the dimension of the vector variable; n is the number of training pairs x i → y i ; σ is the single learning or smoothing parameter chosen during the network training; Y i is a desired scalar output given by the observed input x i .
The topology of GRANN consist of four layers. The first layer is the input layer that is fully connected with second layer. The input neurons are distribution units which provide all the measurement variables X to all neurons of second layer also known as pattern layer. 4 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 The second layer is the first hidden layer and consists of N processing elements or nodes, where N is the number of sample within a training data set and each node represents the input vector, X i , associated with the vector assigned with the j th sample in training data.
In each node, each input vector is subtracted from the vector assigned to the node X j . This difference es then squared by the node and the result is feed into a nonlinear kernel which is usually an exponential function. The pattern unit output are passed to the summation units of third layer which is called summation layer.
The summation layer is the second hidden layer and has two nodes. The input to the first node, as shows eq. 6, is the sum of the pattern layer outputs, each weighted by the observed output yj corresponding to Xj. The input of the second node is the summation of the pattern layer activation.
The fourth layer also known as output layer, receives the two outputs from the summation layer and divides them to yield an estimate of Y, the prediction result.
Opposite to FFBPNN, in GRANN architecture there are no learning and architectural parameters to be determined such as the number of hidden layers, the training algorithm, learning rate, momentum, among others. The only one parameter that must be determined is the smoothing factor, σ , which is applied after the training stage.
The choice of this parameter is very important because affects the smoothing of the training samples. In this sense, small values of σ tend to make each training point distinct whereas large values force a greater degree of interpolation between the training samples [59][60][61][62][63].
In prior works, GRANN were used to solve the neutron spectrum unfolding problem from the count rates measured with the BSS.
The results obtained showed that the use of GRANN to unfold the neutron spectra is a promising alternative approach, however, one of the main drawbacks was the lack of scientific and technological tools based on this emerging technology, capable to be used in real experimental places with high efficency. For this reason, in this research work, the synapse code was developed.

Synapse code development
The Synapse code is composed of three main stages as showed in Figure 1: The the GRANN methodology, the neutron spectra unfolding code based on GRANN and the rates count comming from BSS.

Stage one: GRANN methodology
The GRANN methodology is a set of computer algorithms programmed for training several GRANNs in order to create the network architecture capable to solve the neutron spectrometry and dosimetry problems and for calculating the optimized value of the smoothing factor, σ , which is used in a final GRANN, programmed at the second stage, in order to unfold the neutron spectrum based on the rates count measured with a BBS in experimental places.
The GRANN methodology is composed by three stages as illustrated in Figure 2: the pre-processing of the information of trainig data, the training of several GRANNs and the determination of the critical value of the GRANN, the smoothing factor, σ .

Figure 2. Stage one, automatization process of GRANN methodology
Pre-processing of the training information. Because GRANN is a kind of FFNN with supervised training, a data set with both, inputs and outputs, was required to perform the GRANN training and testing. The data set was obtained from the IAEA's neutron spectrum compendium [67].
The neutron spectrum reported on the IAEA compendium, are defined in lethargy units, and are expressed in 60 energy groups, ranging from thermal neutrons to 630 MeV. As mentioned, the IAEA report also contains information regarded with 15 dosimetric quantities and several survey instruments.
The pre processing stage of the GRANN methodology, showed in Figure 3, was implemented for building the input-output data sets used for training the 5 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 GRANNs. The rate counts were used as entrance data and the neutron spectrum, dosimetric quantities and instrument survey readings are used as output data. Each neutron spectrum was converted from lethargy to energy units using equation 8, and with this information, the BS rates count were calculated.
Where φ E (u) is the neutron spectrum expressed in energy lethargy units, E sup is the superior energy interval and E inf is the inferior energy interval.
As is showed in Figure 3, for calculating the rates count, the neutron spectrum expressed in energy units, extracted from the IAEA compilation, were multiplied with each response matrix (RM).
The RM taken from the IAEA compilation were: the RM for a 3 He neutron detector, calculated by the PTB; the RM for a 3 He neutron detector, calculated by LALN; and the RM for a 6 LiI(Eu) neutron detector, calculated by GSF.
As can be seen on Figure 3, by multiplying the neutron spectrum data set with the fluence to dose and instrument conversion factors, the values of 15 dosimetric quantities and 7 survey instruments were calculated.
After performing the calculations, the rates count for each neutron detector, the equivalent doses and the instruments readings were obtained.
This information was embedded on the Synapse code, and is used for unfolding the experimental neutron spectrum, based on the rates count measured experimentally, using the GRANN technology in which the code is based.

GRANN training and smoothing factor, σ , determination.
Each time the Synapse code is used for unfolding a real experimental neutron spectrum, the three general stages are executed. These stages were automated designing computer programming routines, under the Matlab programming environment.
In order to train and test a GRANN capable to solve the neutron spectrum unfolding problem, a data-set with 251 neutron spectra, 15 dosimetric quantities and 7 measurement instruments, extracted from the IAEA's compilation, were used. 80 % of the whole data-set was used at GRANN training stage and the remaining 20 % was used at testing stage.
For calculating the spread value, the programmed algorithms train and test 2000 GRANN, using the data set calculated at pre-processing stage, with the aim to calculate and to choose the optimized value of the smoothing factor, σ .
Opposite to FFBPNN, GRANNs have a fixed network architecture and the only one parameter to be optimized is the smoothing factor. This feature lets to add new information to the whole database in order to extend the training examples by retraining the network for increasing the knowledge.
The feature of retraining GRANNs, lets to experiment by varying the features of the entrance and output data, i.e., the measured rates count, and the spectrum, equivalent doses and survey instruments respectively, with the aim to reduce the number of BS used at experimental measurements.
By reducing the number of BS in experimental places, the time spent making experimental measurements, and the weight of the whole BSS could be reduced.
To do a retraining using FFBPNNs, is very difficult, mainly because each new training, requires to optimize new learning and architectural parameters of the network, whis is the more serious drawback.
As mentioned, the most important parameter for training GRANNs, is the optimum selection of the spread value, σ . A very large spread value could cause over fit, while a very small value may cause a sub adjustment of the trained network. Therefore, the value of the spread constant is a parameter that has to be selected optimally.
To make a very close adjustment of the data, a spread value smaller than the typical distance between the input vectors is used. To adjust more smoothly, a higher spread value is used.
However, a very large spread value could cause an over adjustment, while a very small value could cause a sub adjustment. Therefore, the constant propagation value can be considered as a regularization parameter that has to be selected optimally.
In this research work, the cross validation technique Leave-one-out [68], was automated as a programming routine on the Synapse code, in order to choose the optimum value of the spread constant. 6 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 The designed computer programming routine selects a single observation from the original sample, maintaining it as the data to validate, and uses the remaining observations as training data. The kernel spread constant is selected in the range of 0 to 2 in steps of 0.01.
For training the GRANNs, 80 % of the whole data set was used at training stage and the remaining 20 % at testing stage. The average time to calculate the optimum value of σ after trainig 2000 GRANNs, is 154 seconds approximately.
As showed on Figure 4, the sum of the mean square error (MSE), is calculated at training and testing stages. After calculating all the testing MSE, the average value is selected as the kernel spread constant or smoothing factor σ .

Figure 4. GRANN training and determination of the smoothing factor
Once each individual neural net is trained using the calculated training data set, the sum of the MSE between each spectrum calculated by the network and the expected one is calculated. As soon as all the MSEs are calculated, the mean is selected as the corresponding value for the specific smoothing factor, σ .
After calculating the optimized spread value, the next stage involves training a final GRANN, as is showed in Figure 5. After creating a final network, based on the 2000 GRANNs previously trained, the code is ready to perform the unfolding of neutron spectrum measured in experimental environments, using the rates count of a BSS as the only entrance data. The training time of the final GRANN is in the order of milliseconds, with an average value 0.058 seconds, which compared to the time used for training FFBPNN is significantly lower.

Stage two: neutron spectra unfolding code based on GRANN
Similarly to the stage one, the second stage is a set of computer algorithms programmed for unfolding the neutron spectrum based on an optimized GRANN which uses as the only entrance data, the rates count measured with a BBS, in real experimental places.
In this stage, as is showed in Figure 6, a final GRANN is trained, using the smoothing factor calculated at stage one, for unfolding neutron spectrum by using the rates count measured in real experimental places with a BSS as the only entrance data. It is important to mention that, in addition to the neutron spectrum, the code was programmed for calculating 15 dosimetric quantities and/or 7 survey instruments values.
The Synapse code was fully automated designing computer programming routines. A Graphical User Interface (GUI) for the end user was also designed with the aim to unfold neutron spectrum in real experimental, work and research places.

Neutron spectrum unfolding with the Synapse code
The unfolding of neutron spectrum in real experimental environments using the Synapse code is done as follows. Figure 7, shows the main window of the Synapse code, where can be seen that the only piece of entrance information, on the part of the end user, are the rates count measured with a BSS with a neutron detector based on 3 He or 6 LiI(Eu).
The first step to operate the Synapse code is the selection of a working directory, for storing the calculations made during the unfolding of the neutron spectrum.
The selection or creation of the working directory is done by clicking the button labeled as "Folder", located on the upper left corner of the main window (Figure 7).
After clicking on the "Folder" button, a window like the shown in Figure 8 will open. This window lets to select a working folder or, alternatively, create a new one.
The main window of the Synapse code also has a text box labeled as "Network Id" that allows assigning 7 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 an identifier to the neutron spectrum unfolding that is being carried out. This information will be stored on a text file, to identify the training carried out, for performing posterior analysis.  The code is able to perform the unfolding of neutron spectrum, from experimental environments, using one of three RM extracted from the IAEA's compendium, which are embedded on the code: 6 Li(Eu) − GSF, 3 He − P T B and 3 He − LAN L.
The main window has a drop-down selection menu, labeled as "System", for selecting the desired RM which will be used to train the embedded GRANN. According to the selected RM, a different configuration of Bonner spheres will be showed as shown on Figure 9.
An important feature of the Synapse code, that demonstrates the prediction and classification power of this technological tool, based on GRANNs, is the fact that the end user does not have to use all the BS shown in Figure 9. The code has the flexibility to allow to the end user to make a selection of specific BS.

Figure 9. Drop-down selection menu for selecting different RM
Unlike the classical techniques, based on traditional numerical methods, GRANNs use statistical methods to perform the classification and prediction of the output data in a single iteration, using the information contained in the training databases.
Because of this, it has been observed that this type of technology has the ability to classify spectra and calculate equivalent doses using less information in the entrance data, that is, fewer Bonner spheres.
At present, experiments are being carried out that show that this type of technology is capable of performing the unfolding of the spectrum using less Bonner spheres as input data.
After selecting the desired BS of the chosen RM, a text box under the BS labels is generated that allows to write the readings taken experimentally with the corresponding BSS, as is showed in Figure 10.
As can be noticed on Figure 10, prior to the training of the GRANNs, in the right side of the main window, there is no information about any trained neural network. After performing the training, a graph appears on the right side of the main window, as is showed in Figure 12.
This graph shows the 2000 GRANN trained in order to choose the smoothing factor that will be used in the final GRANN.
Once the RM was selected, the appropriate number of Bonner Spheres was chosen and the experimental values measured with the BSS were entered, the end user should click on the drop-down menu labeled as "Train", shown in Figure 11, which has the possibility to train GRANNs with the following options: single spectra, single doses, single instruments, spectra and doses, spectra and instruments, doses and instruments and spectra, doses and instruments.
At present, because of difficulty of the programming procedure, only the options single spectra, single doses, single instruments and spectra and doses were programmed on the code. 8 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 Finally, the GRANNs of the Synapse code are ready to be trained by clicking on the button labeled as "Process".
After pressing this button, as is showed in Figure  12, the GRANN is trained and the neutron spectra, equivalent doses or instrument survey, are calculated, according to the selection made in previous stages.
As mentioned, on the right side of the main window ( Figure 12), a graph appears that shows the smoothing factors calculated after training the 2000 GRANNs.

Figure 10. Entering the experimental values measured with BSS
As can be seen, the whole process on the part of the end user, in order to unfold neutron spectrum based on BSS measurements, is to create a working folder, to select the RM of the desired neutron detector, to enter the experimental measured rate counts and to select the desired GRANN training.
After the GRANN training is done, the code generates a text file with the information regarded to the training performed.

Testing and validation of the Synapse code
The final stage of this research work was to apply the designed Synapse neutron spectrum unfolding code, in real experimental environments, with the aim of testing and validating the results obtained with the trained GRANN.
In order to validate the results obtained with the Synapse code in experimental environments, the  unfolded spectrum of both, a 239 P uBe and a 252 Cf neutron sources were calculated and compared with the reference neutron sources taken from the IAEA compendium. 9 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 Following the procedure previously described, the RM of a 6 Li(Eu) − GSF neutron detector was selected as is showed in Figure 12.
After selecting the RM, the experimental rate counts measured with a BSS with a 6 Li(Eu) neutron detector, property of the Unidad Académica de Estudios Nucleares from the Universidad Autónoma de Zacatecas, México, were introduced to the Synapse code as is showed in Figure 12.
It is important to mention that this neutron detector has 7 Bonner spheres with 0, 2, 3, 5, 8, 10 and 12 inches of diameter. For this reason, only these Bonner spheres were elected from the RM-GSF.
Finally, the GRANNs were trained, and the neutron spectrum were calculated by the code.

Figures 13 and 14
show the neutron spectrum unfolded of a 239 P uBe and 252 Cf neutron sources respectively.
As mentioned, the rates count were measured with the BSS property of the Unidad Académica de Estudios Nucleares, México.
In Figure 13, the 239 P uBe reference neutron spectrum, taken from the IAEA compendium, is showed on red line. The spectrum unfolded with the Synapse code is showed in blue line.
The results obtained by using the Synapse code, were compared with the 239 P uBe reference neutron spectrum, taken from the IAEA compendium. As can be seen, the calculated neutron spectrum agrees with the shape and the peak of the maximum energy, when compared with the target one. Figure 14, shows the 252 Cf reference neutron spectrum, taken from the IAEA compendium on red line, compared with the neutron spectrum, calculated by the Synapse code, showed in blue line.
As can be seen, the neutron spectrum unfolded with the Synapse code also agrees with the shape and the peak of the maximum energy of the reference neutron spectrum.
This demonstrates that the Synapse code, solves with high efficiency and generalization capability the neutron spectrum unfolding problem, by using AI technology based on GRANNs.
The code can be applied with success for unfolding neutron spectrum in real experimental places.
It is important to mention that, although the Synapse code is an innovative and a highly technological tool, based on complex technology, the code is easy, friendly and intuitive for the end user, if compared with other codes used nowadays.
From the results obtained after unfolding the neutron spectrum of both, a 239 P uBe and a 252 Cf neutron sources, can be seen that the Synapse neutron spectrum unfolding code, based on GRANN technology is a promising and innovative technological alternative for solving the neutron spectrometry and dosimetry problems, in high energy physics, for radiation protection purposes, and that can be applied with success in real experimental places.

Discussion and conclusions
The use of AI technology in the neutron spectrometry and dosimetry research domain, is a new solution proposal. Previous researches indicate that FFBPNN perform well and this kind of network has been the most popular approach used in this research area. 10 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 The neutron spectra unfolding and calculation of equivalent doses, starting from the rates count coming from a BSS, using FFBPNN technology, has received much attention in recent years due the successful results observed.
However, the intrinsic difficulties, associated with the optimization of the learning and architectural parameters of the networks, make difficult to apply the theories of IA in the field of neutron spectrometry.
The anterior, has motivated the study and development of alternative methodologies with the aim to explore different types of ANN architectures such as GRANNs, that have the characteristics of being nonparametric, that is, unlike FFBPNN, in GRANN is not required to determine and to optimize the entire set of parameters that FFBPNN requires.
Opposite to FFBPNN, GRANN are very flexible and new information can be added immediately with almost no retraining. The biggest advantage is the fact that the probabilistic approach of GRANN works with one-steponly learning and uses a single common radial basis function kernel bandwidth, σ , that is tuned to achieve an optimal ANN learning.
Given the novelty of the approach, it was observed the need of developing scientific and technological tools for the end user, able to solve with high performance and efficiency the problems associated with neutron spectrometry and dosimetry.
Because the technology based on AI is an emerging research domain, specifically using GRANNs, there is a lack of scientific and technological tools to implement it in work, experimental and laboratory environments, in a flexible and efficient way.
In collaboration agreement with the OMADS company the Synapse neutron spectrum unfolding code, based on GRANN technology, was developed.
The code is capable to unfold the neutron spectrum and to calculate 15 different dosimetric quantities using the count rates, coming from a BSS, as the only entrance information.
The code solves the neutron spectrometry and dosimetry problems with high performance and generalization capacity, and the results obtained show that is a promising alternative which can be applied in the solution of these problems.
The Synapse code was fully automated with the aim to unfold neutron spectrum in real experimental, work and research places.
Each time the Synapse code is executed, three general stages are performed. At stage one, in order to calculate an optimized spread value, σ , 2000 GRANN are trained and tested in an average time of 154 seconds approximately.
Once the the optimized spread value is calculated, at stage two and three, the code is ready to perform the unfolding of neutron spectrum measured in experimental environments, using the rates count of a BSS, as entrance data. The training time of the final GRANN is in 0.058 seconds average.
In order to use the Synapse code, which is fully automated, the whole process is to create a working folder, to select the RM of the desired neutron detector, to enter the experimental measured rates count and to select the desired GRANN training. After the GRANN training is done, the code generates a text file with the information regarded to the training performed.
In order to validate the results obtained with the Synapse code in experimental environments, the unfolded spectrum of both, a 239 P uBe and a 252 Cf neutron sources were calculated and compared with the reference neutron sources taken from the IAEA compendium.
The neutron spectrum unfolded with the Synapse code agree with the shape and the peak of the maximum energy of the two reference neutron spectrum.
This demonstrates that the code, solves with high efficiency and generalization capability the neutron spectrum unfolding problem, by using AI technology based on GRANNs, and can be applied with success for unfolding neutron spectrum in real experimental places.
Unlike the classical techniques, based on traditional numerical methods, GRANNs use statistical methods to perform the classification and prediction of the output data in a single iteration, using the information contained in the training databases.
Because of this, it has been observed that this type of technology has the ability to classify spectra and calculate equivalent doses using less information in the entrance data, that is, fewer Bonner spheres.
By reducing the number of BS in experimental places, the time spent for making experimental measurements could be reduced and in consequence, the weight of the whole BSS.
Despite the success of the results obtained with code, some drawbacks were observed. The first one is that the code was developed using the Matlab programming environment.
The main drawback is that it is a private tool, and the source code of AI technology is not available to modify as one wish or need.
Another problem using this environment, is that is not possible to create executable files with the developed ANN technology.
This makes difficult to distribute copies of the code to work-centers or laboratories. In this sense, for executing the Synapse code, the end user must have a Matlab licence which is very expensive.
One more drawback is that the Synapse code cannot be executed using the new technologies of information and communication such as cloud 11 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 05 2020 -10 2020 | Volume 7 | Issue 24 | e3 computing environments, which is a very promising technological alternative.
The synapse code is executed on a standard laptop computer with an i7 processor and 16 GB of RAM. These features are fixed and cannot be modified. Using cloud computing technology to execute the code, the needs of hardware can be changed on the cloud.
Looking for a solution to the mentioned problems, at present, in collaboration agreement wit the OMADS company, work is being done in order to migrate the Synapse code to open-source programming environments, in such a way it can be executed in a cloud computing environment, using new technologies of information and communication tools of the fourth industrial revolution known as Industry 4.0.

Funding
This work was supported by OMADS Co., a research, innovation and technological development enterprise. This work was partially supported by "Fondo Sectorial de Investigación para la Eduación" under contract 241771.