论文标题
LSTM驱动的多孔介质中二氧化碳注入的预测
LSTM-driven Forecast of CO2 Injection in Porous Media
论文作者
论文摘要
模拟多孔介质中多相流的偏微分方程（PDE）的能力对于不同的应用，例如二氧化碳的地质隔离，地下水流量监测和从地质地层中回收碳氢化合物的能力至关重要[1]。可以通过使用各种离散化方案（例如有限元素，有限量，光谱方法等）求解管理PDE的多相流问题。但是，大多数研究人员都专注于模型在模型训练的时空领域内的性能。在这项工作中，我们将ML技术应用于近似PDE解决方案，并专注于训练域之外的预测问题。为此，我们使用两种不同的ML体系结构 - 馈电神经（FFN）网络和基于长期的短期内存（LSTM）神经网络，以根据过去的解决方案的了解来预测未来的PDE解决方案。我们的方法的结果显示在两个示例的PDE上 - 即PDE的一种形式，该形式对二氧化碳的地下注入及其双曲线极限进行了建模，这是一个常见的基准情况。在这两种情况下，LSTM体系结构都具有根据先前数据在未来时间预测解决方案行为的巨大潜力
The ability to simulate the partial differential equations (PDE's) that govern multi-phase flow in porous media is essential for different applications such as geologic sequestration of CO2, groundwater flow monitoring and hydrocarbon recovery from geologic formations [1]. These multi-phase flow problems can be simulated by solving the governing PDE's numerically, using various discretization schemes such as finite elements, finite volumes, spectral methods, etc. More recently, the application of Machine Learning (ML) to approximate the solutions to PDE's has been a very active research area. However, most researchers have focused on the performance of their models within the time-space domain in which the models were trained. In this work, we apply ML techniques to approximate PDE solutions and focus on the forecasting problem outside of the training domain. To this end, we use two different ML architectures - the feed forward neural (FFN) network and the long short-term memory (LSTM)-based neural network, to predict the PDE solutions in future times based on the knowledge of the solutions in the past. The results of our methodology are presented on two example PDE's - namely a form of PDE that models the underground injection of CO2 and its hyperbolic limit which is a common benchmark case. In both cases, the LSTM architecture shows a huge potential to predict the solution behavior at future times based on prior data
