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Machine Learning Exercises on 1-D Electromagnetic Inversion

This work aims to enhance our fundamental understanding of how the measurement setup that is used to generate training and testing data sets affects the accuracy of the machine learning algorithms that attempt to solve electromagnetic inversion problems solely from data. A systematic study is carried out on a 1-D semi-inverse electromagnetic problem, which is estimating the electrical permittivity values of a planarly layered medium with fixed layer thicknesses assuming different receiver–transmitter antenna combinations in terms of location and numbers. The accuracy of the solutions obtained with four machine learning methods, including neural networks, is compared with a physics-based solver deploying the Nelder–Mead simplex method to achieve the inversion iteratively. Numerical results show that: 1) deep-learning outperforms the other machine learning techniques implemented in this study; 2) increasing the number of antennas and placing them as close as possible to the domain of interest increase inversion accuracy; 3) for neural networks, training data sets created on random grids lead to more efficient learning than the training data sets created on uniform grids; and 4) multifrequency training and testing with a few antennas can achieve more accurate inversion than single-frequency setups deploying several antennas.