Including uncertainty is essential for accurate decision-making in underground applications. We propose a novel approach to consider structural uncertainty in two enhanced geothermal systems (EGSs) using machine learning (ML) models. The results of numerical simulations show that a small change in the structural model can cause a significant variation in the tracer breakthrough curves (BTCs). To develop a more robust method for including structural uncertainty, we train three different ML models: decision tree regression (DTR), random forest regression (RFR), and gradient boosting regression (GBR). DTR and RFR predict the entire BTC at once, but they are susceptible to overfitting and underfitting. In contrast, GBR predicts each time step of the BTC as a separate target variable, considering the possible correlation between consecutive time steps. This approach is implemented using a chain of regression models. The chain model achieves an acceptable increase in RMSE from train to test data, confirming its ability to capture both the general trend and small-scale heterogeneities of the BTCs. Additionally, using the ML model instead of the numerical solver reduces the computational time by six orders of magnitude. This time efficiency allows us to calculate BTCs for 2′000 different reservoir models, enabling a more comprehensive structural uncertainty quantification for EGS cases. The chain model is particularly promising, as it is robust to overfitting and underfitting and can generate BTCs for a large number of structural models efficiently.

中文翻译：

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用于裂缝性油藏稳健结构不确定性量化的机器学习

包含不确定性对于地下应用中的准确决策至关重要。我们提出了一种使用机器学习（ML）模型来考虑两个增强型地热系统（EGS）中的结构不确定性的新方法。数值模拟的结果表明，结构模型的微小变化可能会导致示踪剂突破曲线（BTC）发生显着变化。为了开发一种更稳健的方法来包含结构不确定性，我们训练了三种不同的机器学习模型：决策树回归（DTR）、随机森林回归（RFR）和梯度增强回归（GBR）。 DTR 和 RFR 可以一次性预测整个 BTC，但它们很容易出现过拟合和欠拟合的情况。相比之下，GBR 将 BTC 的每个时间步长预测为单独的目标变量，考虑到连续时间步长之间可能存在的相关性。该方法是使用一系列回归模型来实现的。该链模型从训练到测试数据的 RMSE 实现了可接受的增长，证实了其捕获 BTC 的总体趋势和小规模异质性的能力。此外，使用 ML 模型代替数值求解器可将计算时间减少六个数量级。这种时间效率使我们能够计算 2’000 个不同油藏模型的 BTC，从而能够对 EGS 情况进行更全面的结构不确定性量化。链模型特别有前途，因为它对过拟合和欠拟合具有鲁棒性，并且可以有效地为大量结构模型生成 BTC。