# High Dielectric Design of Polymer Composites by Using Artificial Neural Network
## 3 Results & Discussions
### Correlation Analysis of Variables  
The Pearson coefficients between various input parameters and composite's \(\varepsilon_{r}\) were calculated to discover the key factors, as shown in Figure 6. The Pearson coefficient ranges from \(-1\) to \(1\) with \(-1\) representing the strongest negative correlation and \(1\) representing the strongest positive correlation [53]. The largest positive correlation to \(\varepsilon_{r}\) is dominated by \(\varepsilon_{r}\) and filler's volume fraction, while the most negative correlation comes from shell's thickness. The \(\varepsilon_{rf}\) has also a positive correlation to \(\varepsilon_{r}\), but considering that the correlation  
Figure 4: Training and validation loss curves of the ANN over epochs. Figure 5: Dielectric constant prediction accuracy between ML prediction vs. experimental values from (**a**) original dataset and (**b**) modified dataset. coefficient of \(\varepsilon_{rm}\) is higher than that of \(\varepsilon_{rf}\), it can be seen that the dielectric constant of the polymer matrix is more dominant to increase the dielectric constant of the composite. On the other hand, the operating frequency and thickness of the shell are negatively correlated with \(\varepsilon_{r}\). The shell plays a role to compensate a dielectric mismatch between polymer matrices and ceramic fillers in core-shell structure. It shows that the shell is important for the purpose of increasing breakdown strength, but it is consistent with the results of previous studies that it plays a negative role in terms of increasing dielectric constant [54]. In polymer-based composites, the dielectric constant of the composites primarily depends on the dielectric constant of the matrix and filler, and filler's volume fraction as shown in Figure 6. The combined effect of the dielectric constant of matrix and filler, and the volume fraction of filler on composite's dielectric constant was studied using the ANN as shown in Figure 7a-c. When we set the \(x\)-axis and \(y\)-axis with the main variables, the other variables are fixed based on the most overlapping data, with a filler diameter of 200 nm, a filler dimension of 1D nanowire, a frequency of 1 kHz, and without a core-shell structure. Figure 7a,b show the combined effect of the dielectric constant of matrix and filler, and the volume fraction of filler, respectively. As we can estimate, the dielectric constant of the composite shows a typically proportional tendency to increase as the dielectric constant of the matrix and the volume fraction of the filler increase. In Figure 7b, there are some distortion contour lines. It is derived from insufficient data with the dielectric constants of filler between about 500 and 800. Despite the lack of data, it shows the tendency of the composite's dielectric constant to generally increase as the dielectric constant and the volume fraction of the filler increase. When matrix and filler's dielectric constant are considered together in Figure 7c, it shows the same tendency as in Figure 7a,b that composite's dielectric constant increases as matrix and filler's dielectric constant increase. Furthermore, it is presented to discuss the effect of minor variables such as filler's diameter and shell's thickness in Figure 7d,e. When it comes to filler's diameter, the dielectric constant of the composite represents a general tendency to decrease as the filler's diameter decreases. This is mainly attributed to the lowered dielectric constant of filler caused by decreasing particle size. The dielectric constant of nanof fillers decreases with decreasing particle size due to depolarization fields, surface properties, electrical boundary conditions, and defects [55]. As for the effect of the shell's thickness, it shows the tendency of the composite's dielectric constant to decrease as the shell's thickness increases. This is because in the core-shell structure, the shell reduces the high electrical mismatch between the filler and the matrix.