## 2 Problem Statement
To make the solution of to the problem universally applicable, let us replace the variables:  
\[\widetilde{\lambda}_{i}=\frac{\lambda_{i}-\lambda_{L}}{\lambda_{L+M-1}-\lambda_{L }},\ \ \widetilde{R}_{i}=\frac{R_{i}-\min(\mathbf{R})}{\max(\mathbf{R})-\min( \mathbf{R})}, \tag{1}\]  
thus moving the input data into the range of amplitude and wavelength variation from 0 to 1. In Equation (1), the set \(\mathbf{R}\) denotes the set of reflection coefficients \(R_{i}\), \(i=0.509\), belonging to the wavelength range \(\lambda\in[1510,\,1595]\) nm. Let us omit the tilde sign for normalized data to make future recording easier. We also assume that we are dealing with normalized values by default. The normalization of the spectrum values by wavelength and amplitude enabled us to make the solution universal and apply it to FBG wavelength determination in any frequency range, assuming the similarity criterion was met. An elementary dataset is a collection of \(M\) normalized discrete values of the spectrum \(\{R_{i}\}\) (\(i=0,M-1\)) obtained through mathematical modeling. The target value of the central wavelength \(\lambda_{\text{B}}\) corresponds to this dataset. As a neural network, we used one of the most commonly used architectures in data approximation, linear and nonlinear regression problems--a three-layer Rosenblatt's perceptron with variable S-A connections [41]. The three layers were sensory S (input), associative A (hidden), and response R (output). A distinguishing feature of Rosenblatt's perceptron with sequential links is the synaptic connectivity of each neuron of the current layer with all neurons of the next layer [41]. Only associative and response layers can be trained in this configuration. The computational model used in this problem was configured from 19 elements of the sensory layer, 10 elements of the associative layer, and one element of the response layer, as shown in Figure 2.  
The computational difficulty of the proposed neural network can be estimated by counting the number of multiplication and addition operations required. For example, the direct signal propagation algorithm through the neural network can be estimated as \((n-1)\) matrix multiplications and \((n-1)\) vector additions, where \(n\) is the number of model layers. Therefore, the multiplicative computational complexity of the algorithm is defined as \(\mathsf{O}(w)\), and the arithmetic complexity is of the order \(\mathsf{O}(2w+v)\), where \(w\) is the number of synaptic connections and \(v\) is the number of neuron shifts equal to the number of neurons of the associative and response layers. Thus, for the neural network used, the computational  
Figure 1: A diagram of the same FBG spectrum in two positions. The red line represents the unperturbed state, while the blue line represents the shifted state; dotted lines denote the discretized spectrum, and solid lines denote the true (continuous) spectrum. complexity was O(288). This value ensures near-instantaneous network response, which is especially important when running real-time sensor systems. The problem was simplified to calculating the true FBG center wavelength with an error less than \(\sim\)\(\Delta\)\(\cdot\)10\({}^{-3}\), having only spectrum data \(\{\lambda_{i},R_{i}\}\) (\(i=0,M-1\)).