## 3 Results and Discussion
### Deconvolution of the Tunneling-Current Density Maps  
For an efficient design of neuromorphic structures, one should be able to extract the charge density map as accurately as possible. Using a second STM tip, one can create a tunneling current map strongly correlated with the charge density image. The rather intricate tunneling process between the active layer and the tip can be considered, in a first approximation, as a convoluted image of the ground state density and filter associated with the tip geometry. Assuming that the filter function is not known, we investigate how far the general purpose image-to-image translation method used to map potentials to charge densities can be also used to perform deconvolutions, i.e., a mapping from the tunneling current back to the charge density. This would be significant, as the tunneling current map represents the information directly accessible from experiment. We investigate several scenarios with respect to the convolution filters as described in Figure 7. The ideal case corresponds to a two-dimensional Gaussian filter with equal standard deviations \(\sigma_{x}=\sigma_{y}=\sigma\). Starting with a small value \(\sigma=1\), we have only a slight change in the TCM compared to the reference CDM. As a result, we can see that the prediction matches the original very well. Increasing the blurring effect, by using a larger standard deviation \(\sigma=3\), we have an enhanced dispersion of the maxima in the input TCM. However, the image translation method provides a similar accuracy, as the kernel is symmetric. Asymmetric kernels, with the larger standard deviation on either the \(x\)-direction (\(\sigma_{x}=3\), \(\sigma_{y}=1\)) or on the \(y\)-direction (\(\sigma_{x}=1\), \(\sigma_{y}\)), do not induce a visible degradation of the prediction accuracy. The Gaussian kernel is thus easily recognizable by the cGAN approach. Instead, the noise has a more significant impact. A symmetric kernel (\(\sigma_{x}=\sigma_{y}=1\)), which, in addition, has a noise component with \(\sigma_{n}=0.1\), transforms the CDM into a rather different map. In this case, although, overall, the predicted image well resembles the reference, the prediction accuracy is visibly lower as it is seen by comparing the prominent maxima located at the branching area. A similar result is obtained for an asymmetric kernel (\(\sigma_{x}=3\), \(\sigma_{y}=1\)), which further confirms the influence of the noise on the prediction accuracy. This single example, however, cannot conclusively establish the relative importance of the two factors. Figure 6: The input-output commutation using a rotating in-plane electric field \(\vec{E}_{0}\), with components \(E_{x,i}=-E_{0}\cos(\theta_{i})\) and \(E_{y,i}=-E_{0}\sin(\theta_{i})\), with \(E_{0}>0\). The \(\theta_{i}\) angle starts from \(\pi/2\), i.e., the electric field is initially oriented along the \(-y\) direction and it is decreasing in steps of \(\pi/10\). The first row of images ends with the field oriented along the \(+y\) direction. A switching between the input and output terminals is achieved, as well as the splitting of the charge distribution across pairs of input terminals. In order to obtain a quantitative statistical image on the performance of the image-to-image translation method, the \(R^{2}\) coefficient of determination is calculated on a test set of 100 samples, generated per each set of conditions. Figure 8 evidences the main conclusions drawn from the results obtained for the selected test structure discussed before. For symmetric as well as asymmetric Gaussian kernels with no noise, \(R^{2}\) coefficients of \(\sim\)0.9 can be achieved. As the noise is switched on, significantly lower values are obtained: for the symmetric case, \(R^{2}\simeq 0.72\), while for the asymmetric case, \(R^{2}\simeq 0.57\). This statistical evaluation of the prediction accuracy shows that indeed both factors, kernel asymmetry and noise, impact the prediction accuracy.