## 3 Results  
Table 1 summarizes the number of neurons for the different models. The ideal number of neurons was determined in a trial and error way, aiming for the best performance of the MSE while keeping the number of neurons small. The number of delays of the NARX model was determined in the same way. As objective function, the mean squared error (MSE) was used for all the models. While the input differs for each model (see Table 1), the element stress or the base force were used as feature data for all ANN. Furthermore, except for the biLSTM, the Nguyen-Widrow layer initialization function [18] was used to generate the initial weights and biases of the neurons for all ANNs. For the biLSTM, the input weights were initialized with the [PERSON]/[PERSON] initializer [19], using an orthogonal initialization for the recurrent weights, while the forget gate bias was initialized with ones and the remaining biases with zeros. All models also share the same activation function, namely the hyperbolic tangent sigmoid, except for the biLSTM, which uses the sigmoid function for the gate, the hyperbolic tangent function for the cell state and hidden state, and the linear activation function for the regression layer. The used training algorithm is also indicated in Table 1.  
Figure 5: NIRSpec module’s optical bench with the ten most stressed elements highlighted, with a perspective from below in order to depict all ribs stiffening the bench. The NARX model was designed in open-loop form, where the input targets were used as feedback features. The model used as many inputs as sensors and had one hidden layer, a defined number of delays, and one output layer per stress (see Table 1). The network with a biLSTM layer consisted of a sequence input layer with as many neurons as inputs, followed by a biLSTM layer. Then, there was one fully connected layer and, lastly, the regression output layer with its linear activation function and as many neurons as outputs. After the setup of the architecture of the different models, they were trained on the setting as listed in Table 1. Figure 6a,b shows an example of the learning curves for the pretrained ANN and the NARX model for the industrial use case, respectively. The blue curves represent the MSE over the training epochs for the training data, the green curves represent the error for the validation error, and the red line represents the error for the test data. The green circle marks the optimal validation performance. The training curves of every model decrease (as clearly shown in Figure 6 for the pretrained ANN and the NARX model), indicating that the models are able to learn the underlying data. The remaining gap between the validation curves and the training curves can be ascribed to the generalization of the data. As the final validation error is not too large, training can be concluded to be successful. After the training, the models were deployed on the test data. The results of their predictions can be seen in the following section. The evaluation of the training on the theoretical cases shows that the NARX model is extremely sensitive to the resolution of the frequency range. Dividing the frequency range into 600 rather than