# Increasing the Reliability of Flood Embarments with Neural Imaging Method
## 5 Results and Discussion
Zero means no error. The training dataset the lowest training error, which is common and correct. The low MSE for the training dataset indicates the best-fit of the network to training data. Figure 11: Training data division and single neural network training results: (**a**) training, validation and test samples, (**b**) mean squared error and the level of regression values. Figure 10: Model of a neural network cluster generating 2012-point resolution output image. Another tested network quality indicator was a regression, R. When R is equal to 1, this means a close relationship, while 0 indicates a random relationship. As it can be observed in Figure 12b, the value of R in the three cases is close to 1. This can particularly be observed in the test and validation sets, which is very favorable. When the values are close to 1, this indicates good fitting of ANN results (output vectors) to patterns in individual datasets (training, validation and test). Figure 12 shows the correlation diagrams for the analyzed network. It can be observed that the number of results that go beyond the reference lines is small, and their correlation is high. This is proved by the overlapping correlation lines for all the examined cases: The training, validation, and test sets, and for the total of all three sets. Figure 13 shows three plots for ANN training parameters versus epochs (pass of all the training data through one iteration loop). It can be seen that network training process ended with Epoch 43. The gradient plot shows that the gradient value was stable for several preceding epochs (the dynamics of change was close to zero). Examining a similar point in the momentum--plot one can observe that--it reaches its minimum value at Epoch 37 and that the value does not change over successive six epochs. The last (bottom) curve in the plot denotes the number of preceding epochs that did not improve the validation deviation. It was assumed that if the validation error does not decrease after  
Figure 12: Data correlation in ANN (artificial neural networks) training, testing and validation. six successive epochs, then the training process should be stopped. That is why, the training process ended at Epoch 43. Figure 14 shows the plot of mean squared error recorded during artificial neural network training. It can be observed that the MSE values are low and there are no major variations in plot shape, which points to the lack of network overfitting and, at the same time, to high effectiveness of the designed system for tomographic image reconstruction. Figure 15 shows the error histogram plot for the network outputs and the patterns. The vertical bars in the plot represent deviations from the pattern. It can be noted that the highest deviations are  
Figure 14: Plot of mean squared error in neural network training. Figure 13: Plots of selected parameters in ANN training. very low, close to zero. The shape of the histogram resembles that of a normal distribution curve. In addition, this indicates a high quality of the produced solution. Figure 16 shows a comparison between the patterns and the outputs generated by the designed neural tomographic system. Reconstructed images are shown on the right. Figure 16: Comparison of patterns and outputs. Figure 15: Neural network training error histogram plot. Comparing the output images with their patterns one can clearly notice a high convergence of details. The concentration of colors in specified pixels allows for the assessment of location, size, intensity, range and expansion direction of the overflow.