# Phased Antenna-Array Synthesis Using Taylor-Series Expansion and Neural Networks
## 5 Neural Networks for Synthesis and Optimization of Antenna Arrays
### Benefits of the Taylor-Neural Network Architecture
In this figure, the distances between the weight vectors of neighboring neurons in the SOM are represented. Each neuron in the SOM has an associated weight vector that represents the characteristics of the data points it maps to. The distances between these weight vectors indicate how similar or different the neurons are in terms of the data they represent. A smaller distance between two neurons suggests that the data points associated with those neurons are similar to each other, while a larger distance indicates greater dissimilarity. This figure likely shows a heatmap or a color-coded representation of the weight distances, where the colors represent the magnitude of the distances. A well-organized SOM would show smaller distances between neurons that are closer to each other on the map, indicating good clustering of similar data points. This figure is crucial for evaluating how the SOM algorithm has grouped the data and how well the structure of the dataset has been captured. Figure 33 presents the sample hits for the Taylor method dataset. Sample hits refer to the number of data points that have been mapped to each individual neuron in the SOM. In this context, the figure shows a visualization of how frequently each neuron has been activated via the input samples. A high number of hits for a particular neuron indicates that the neuron has been frequently activated via similar data points, suggesting that the neuron represents a dense region or cluster of the dataset. Conversely, a neuron with fewer hits may represent a region in the dataset that is sparsely populated or less representative of the overall data distribution. This figure helps assess the distribution of data across the SOM grid, with areas of the map that have a high number of hits corresponding to well-represented regions of the data. The distribution of hits across the map also reveals how well the SOM has managed to generalize the data into different regions, providing insights into the quality of the clustering. A uniform distribution of hits would indicate a balanced representation of the dataset, whereas a skewed distribution could suggest that some regions of the data are underrepresented or overrepresented in the map. Please refer to the Appendix A for detailed data. Figure 31: Taylor-neural network training; R = 0.99999. In addition to the benefits discussed above, scalability and future application domains must also be considered. While the current study validates the proposed framework on a 16-element linear array operating at mmWave frequencies (28.14 GHz and 37.88 GHz), the architecture is designed to be scalable and adaptable to more complex configurations, including arrays with 64 elements or more. At such scales, mutual coupling, nonlinear interactions, and hardware-induced uncertainties become more pronounced. These effects can be addressed in future work by incorporating domain-specific mitigation strategies--such as inter-element spacing adjustments, electromagnetic decoupling techniques, or the use of engineered metasurfaces--into the neural network's training dataset. Furthermore, we aim to extend the applicability of this approach to THz-band antenna arrays, where fabrication tolerances, material dispersion, and surface-wave effects require more intricate modeling. By retraining the network with simulation or measurement-based data that reflect these challenges, the proposed method has the potential to remain robust across a wide range of real-world deployment scenarios. Figure 33: Sample hits. Figure 32: SOM-neighbor weight distances. Beyond scalability, we also recognize that the current focus on uniform linear arrays may limit the generalization of the method to more complex array geometries. Many practical applications involve non-linear configurations, such as conformal, sparse, or irregular arrays--especially in aerospace, vehicular, and satellite systems.