用于地热模型高效预测与不确定性量化的数据空间反演
Data Space Inversion for Efficient Predictions and Uncertainty Quantification for Geothermal Models
AI总结：
本文提出将数据空间反演（DSI）应用于地热储层建模，通过修改DSI算法直接从后验预测分布采样，在不估计模型参数的情况下高效实现预测与不确定性量化。
摘要：
以量化的不确定性进行准确预测的能力，为地热储层的成功管理提供了关键基础。使用地热储层模型进行预测的常规方法涉及利用现场数据估计未知的模型参数，然后将这些估计中的不确定性传递到感兴趣的预测量中。然而，未知参数并不总是直接关注的对象；相反，预测才是首要重要的。数据空间反演（DSI）是一种替代方法，它允许在量化不确定性的情况下高效估计感兴趣的预测量，从而完全避免了对模型参数进行估计的需要。在本文中，我们阐述了DSI在地热储层建模中的适用性。我们首先从贝叶斯视角回顾了模型校准、预测和不确定性量化的过程，并引入数据空间反演作为一种简单、高效的技术来近似后验预测分布。然后，我们对典型的DSI算法进行了修改，使我们能够直接且高效地从DSI近似中采样以获得后验预测分布，并将该算法应用于地热储层建模中的两个模型问题。我们评估了我们的DSI算法相对于其他常见不确定性量化方法的准确性和效率，并研究了储层模型模拟次数如何影响对后验预测分布的最终近似。我们的结果表明，数据空间反演是一种稳健且高效的技术，能够利用地热储层模型进行具有量化不确定性的预测，为更常规的方法提供了有用的替代方案。
英文摘要：
The ability to make accurate predictions with quantified uncertainty provides a crucial foundation for the successful management of a geothermal reservoir. Conventional approaches for making predictions using geothermal reservoir models involve estimating unknown model parameters using field data, then propagating the uncertainty in these estimates through to the predictive quantities of interest. However, the unknown parameters are not always of direct interest; instead, the predictions are of primary importance. Data space inversion (DSI) is an alternative methodology that allows for the efficient estimation of predictive quantities of interest, with quantified uncertainty, that avoids the need to estimate model parameters entirely. In this paper, we illustrate the applicability of DSI to geothermal reservoir modelling. We first review the processes of model calibration, prediction and uncertainty quantification from a Bayesian perspective, and introduce data space inversion as a simple, efficient technique for approximating the posterior predictive distribution. We then introduce a modification of the typical DSI algorithm that allows us to sample directly and efficiently from the DSI approximation to the posterior predictive distribution, and apply the algorithm to two model problems in geothermal reservoir modelling. We evaluate the accuracy and efficiency of our DSI algorithm relative to other common methods for uncertainty quantification and study how the number of reservoir model simulations affects the resulting approximation to the posterior predictive distribution. Our results demonstrate that data space inversion is a robust and efficient technique for making predictions with quantified uncertainty using geothermal reservoir models, providing a useful alternative to more conventional approaches.
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