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We introduce NAMSG, an adaptive first-order algorithm for training neural networks. The method is efficient in computation and memory, and is straightforward to implement. It computes the gradients at configurable remote observation points, in order to expedite the convergence by adjusting the step size for directions with different curvatures in the stochastic setting. It also scales the updating vector elementwise by a nonincreasing preconditioner to take the advantages of AMSGRAD. We analyze the convergence properties for both convex and nonconvex problems by modeling the training process as a dynamic system, and provide a guideline to select the observation distance without grid search. A data-dependent regret bound is proposed to guarantee the convergence in the convex setting. Experiments demonstrate that NAMSG works well in practical problems and compares favorably to popular adaptive methods, such as ADAM, NADAM, and AMSGRAD.

Due to the complexity of unconventional reservoir measurement, log data acquired are often incomplete, which results in inaccurate formation evaluation and higher operational risks. Common solutions, such as coring, are typically high cost related while not being sufficiently representative. In recent years, neural network has received increasing attention given its strong ability in data prediction. Nevertheless, most neural networks only focus on one specific feature of the selected data, thus prohibiting their prediction accuracy for reservoir logs where data are often dominated by more than one key feature. To address this challenge, a novel multi-channel hybrid Long Short-Term Memory (LSTM) neural network for effective acoustic log prediction is proposed. The network combines Convolutional Neural Network (CNN) and LSTM, where CNN is used to extract spatial features of the logs and LSTM network extracts temporal features with the assistance of an adaptive attention mechanism implemented for key feature recognition. In addition, the strong heterogeneity of unconventional reservoirs also increases the difficulty of prediction. Therefore, according to the characteristics of the unconventional reservoir, we designed three feature enhancement methods to mine the hidden information of logs. To prove the performance of the proposed network, a case study is presented with data acquired from Jimusar Oilfield, one of the largest unconventional reservoirs in China. Four groups of experiments are conducted, and the proposed network is employed for acoustic log prediction. The predicted results are validated against measurement (R2: 92.27%, 91.42%, 93.31%, and 92.03%; RMSE: 3.32%, 3.92%, 3.06%, and 3.53%). The performance of the proposed network is compared to other networks such as CNN, LSTM, CNN-LSTM, and random forest (RF). The comparisons show that the proposed network has the highest accuracy level of prediction, which means it provides an effective approach to complement missing data during complicated unconventional reservoir measurement and, therefore, could be of significant potential in energy exploration.