Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: a) once trained, they enable to solve an inverse problem in a fraction of a second, which is convenient for borehole geosteering operations as well as in other real-time inversion applications. b) DL methods exhibit a superior capability for approximating highly-complex functions across different areas of knowledge. Nevertheless, as it occurs with most numerical methods, DL also relies on expert design decisions that are problem specific to achieve reliable and robust results. Herein, we investigate two key aspects of deep neural networks (DNNs) when applied to the inversion of borehole resistivity measurements: error control and adequate selection of the loss function. As we illustrate via theoretical considerations and extensive numerical experiments, these interrelated aspects are critical to recover accurate inversion results.

中文翻译：

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钻孔电阻率测量深度学习反演的误差控制和损失函数

深度学习 (DL) 是一种近似函数的数值方法。最近，它的使用对计算力学中的多个问题的模拟和反演变得很有吸引力，包括石油和天然气应用中钻孔测井测量的反演。在这种情况下，DL 方法表现出两个关键的吸引人的特征：a) 一旦经过训练，它们就可以在几分之一秒内解决反演问题，这对于钻孔地质导向操作以及其他实时反演应用很方便。b) DL 方法在逼近不同知识领域的高度复杂函数方面表现出卓越的能力。然而，与大多数数值方法一样，深度学习也依赖于针对特定问题的专家设计决策，以获得可靠和稳健的结果。在此处，我们在应用于钻孔电阻率测量的反转时调查深度神经网络（DNN）的两个关键方面：误差控制和充分选择损耗功能。正如我们通过理论考虑和广泛的数值实验所说明的那样，这些相互关联的方面对于恢复准确的反演结果至关重要。