Machine Learning Exercises on One Dimensional Electromagnetic Inversion

Abstract : This work aims to enhance our fundamental understanding of how the measurement setup used to generate training and testing datasets affects the accuracy of the machine learning algorithms that attempt solving electromagnetic inversion problems solely from data. A systematic study is carried out on a one-dimensional 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. 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 (i) deep-learning outperforms the other machine learning techniques implemented in this study, (ii) increasing number of antennas and placing them as close as possible to the domain of interest increase inversion accuracy, (iii) for neural networks, training datasets created on random grids lead to a more efficient learning than the training datasets created on uniform grids, and (iv) multi-frequency training and testing with a few antennas can achieve more accurate inversion than single-frequency setups deploying several antennas.
 ? A possible alternative lies in inversion based on deep neural networks, which are capable of learning deep representations and identifying complex patterns in data. ? This is of particular importance for large real datasets where complex data interactions are difficult or even impossible to specify within existing models. ? In this study, we explored the potential of DL based inversion with two 1D EM problems and showed that deep CNN can accurately reconstruct the resistivity distribution in the subsurface from measured data.
 Amongst the first published implementations was the use of a Hopfield neural network, which is a recurrent neural network, for microwave impedance matching72. Through an iterative process, the network could specify how changes in stub position and length could improve network matching. Network weights were determined not through a training process, but by known relationships between stub position and network matching determined from simulations. While this demonstration did not entail a classical trainable discriminative network, it showcased the early potential of neural networks in electromagnetics problems.
 ? In this study, we apply deep convolutional neural networks for 1D inversion of marine frequency-domain controlled-source electromagnetic (CSEM) data as well as onshore timedomain electromagnetic (TEM) data. ? Our approach yields accurate results both on synthetic and real data and provides them instantaneously. ? Using several networks and combining their outputs from various training epochs can also provide insights into the uncertainty distribution, which is found to be higher in the regions where resistivity anomalies are present.The proposed method opens up possibilities to estimate the subsurface resistivity distribution in exploration scenarios in real time.
 ? Visualization of the method of principle components analysis, where a hyperplane in the full design space of grating couplers defines a low-dimensional subspace of high performance devices. ? Dimensionality reduction of images of devices is performed by encoding the image into a Fourier representation and then cropping that representation. ? Schematic of an autoencoder neural network. ? The encoder transforms input data to low dimensional latent vectors while the decoder attempts to reconstruct the input data from the latent vectors with minimal distortion.
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