## 1 Introduction
Neural networks have been successfully applied in various domains, such as image and speech recognition, natural language processing, and autonomous driving. Their ability to model complex relationships and learn from large datasets makes them a powerful tool for addressing the intricacies of electric cleanliness in space missions. By leveraging neural networks, researchers and engineers can develop more efficient and effective methods for predicting, monitoring, and mitigating electric interference in real-time scenarios. In this work, neural networks (Electric Dipole Model Networks--\(EDMnet\)) were used to approximate the inverse function of the MDM electric field problem, as they constitute an efficient method of solving complex and non-linear equations. The problems of (i) the electromagnetic characterization of actual space units and (ii) the development of accurate models able to virtually represent these actual units with equivalent dipole sources, are addressed herein. This is very important at the early steps of a space mission design, in order for the engineers to optimally locate the equipment on the spacecraft hull, ensuring minimum electromagnetic interference issues. In this way, (i) a pre-compliance process was taken for each unit under test and (ii) dedicated measurements (14 measurements for different angles and unit orientations) were performed according to the referred herein process. Using this measurement dataset the solution of the inverse electromagnetic problem yields the best dipole that accurately represents the unit's electromagnetic behavior; i.e., matches the measurement dataset. As stated, this solution is obtained either heuristically or statistically. Both these methods are post-process, due to their time-consuming nature. Additionally, this work presents a machine learning methodology (ANN), as depicted in Figure 1, to find the optimum inverse function for the specific measurement setup based on simulated data. Thus, when the ANN is optimally trained for the specific measurement setup, the inverse calculation (for the actual measurement dataset) is a matter of nanoseconds, instead of a couple of minutes needed for the heuristic approach. Neural networks can learn to approximate functions of arbitrary complexity based on training data, i.e., the inputs and outputs of the function. The neural network training was performed by analyzing artificially generated datasets from the electric field equation in vector form at various positions, as discussed in the next section. The inputs of the proposed \(EDMnet\) were the electric field vector values, for the specific measurement setup, and the outputs were the parameters of the dipole sources (electric dipole position, and electric moment vectors). During training, the weights of the network are evaluated iteratively in order to minimize a predefined loss function that compares the target (artificial dipole) and predicted output values, i.e., predicted dipole parameters. In contrast to heuristic approaches, in which the exploration of a solution space is time-consuming as the algorithm attempts iteratively to identify the set of dipole parameters that best fit the measurement dataset, a pre-trained neural network offers a direct, instant, real-time evaluation of the solution (straightforward calculation of the dipole parameters) during the measurement campaign, enabling system level predictions regardless of the system architecture complexity. The core idea of this work is that for a custom measurement setup, such as the one presented herein and studied in the authors' previous work [2], an ANN (i.e., the inverse dipole field equation for the specific measurement setup) pre-trained with simulated data, can instantly and accurately predict the radiating source based on field measurements. Moreover, in a continuous measurement data stream the ANN architecture is capable of providing a direct stream of results.