GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 resistivity models from the prior distribution, we calculated their corresponding data. The L2-norm of the difference between these and the observed data gives the data misfit values to be used as target output in the training phase. Each simulated model is then compressed performing a 2D DCT. The compression operation consists of the selection of the low order coefficients along both horizontal (first) and vertical (second) direction (or dimension) on which DCT acts: the first coefficients in both dimensions of the compressed space are retained, whilst the others are set to zero. We establish the optimal number of DCT coefficients to consider by calculating the explained variability as the number of retained basis functions along the two DCT dimensions increases. The explained variability is defined as the ratio between the standard deviations of the approximated and the uncompressed true model. The retained coefficients for each simulation represent the input of the CNN, which is now ready to be trained. This procedure is then inserted in a GA inversion framework in which, at every iteration (or generation), a population of DCT compressed models is evaluated. Using the CNN to predict data misfit, we avoid the forward modelling computation for all individuals evaluated during the GA inversion. Synthetic inversion To test the ML-based inversion, we use a synthetic resistivity model corresponding to an area extending for 35 m horizontally and 5.5 m depth. It is discretized in 35x11=385 cells. To calculate the simulated data, we use a Finite Elements forward modelling (Karaoulis et al. , 2013) which simulates an acquisition using 36 electrodes 1 m spaced with the Wenner configuration. This results in 198 data points distributed on 11 levels. The investigations on the spatial variability of the true model led us to use 10 coefficients along the first dimension and 4 on the second, enough to properly reconstruct about 98% of the true model’s variability. So the 385-D model space is compressed in a 40-D one. For the main GA settings, we follow what is suggested in Aleardi and Mazzotti (2016), adopting a number of individuals per population 8 times the number of unknowns. As these are the 40 retained DCT coefficients, each generation includes 8x40=320 models. We provide the algorithm with an initial population of models generated like the training dataset and set the search range for each of the 40 parameters from the minimum to the maximum value of the corresponding DCT coefficient in this starting population. For a complete explanation of the GA parameters see Pohlheim (2006). The tests conducted to determine network architecture and training parameters led us to train the CNN with 15000 models (85% reserved for the training phase and 15% for assessing the network’s performance). In particular, the test regarding the number of models to use is planned in order to find a trade-off between the performance of the training (and of the subsequent ML-based inversion) and the computational time, that must be lower than the one of the standard GA inversion to make the proposed method useful. We perform the inversions through Matlab codes running in parallel on 20 cores of a server equipped with two deca-core Intel Xeon E5-2630 v4 @ 2.20 GHz with 128 Gb RAM. To have more reliable results, we carry out 10 inversions and then average to obtain the DCT coefficients of the best misfit model. We stop the inversions after 100 generations, enough for the algorithm to converge. The comparison (Fig. 2) between the standard inversion (GA) and the one based on ML