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Constrained pressure-temperature residual (CPTR) preconditioner performance for large-scale thermal CO $$_2$$ injection simulation 用于大规模一氧化碳_2$$注入热模拟的受限压力-温度残差(CPTR)预处理器的性能
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-05-01 DOI: 10.1007/s10596-024-10292-z
Matthias A. Cremon, Jacques Franc, François P. Hamon

This work studies the performance of a novel preconditioner, designed for thermal reservoir simulation cases and recently introduced in Roy et al. (SIAM J. Sci. Comput. 42, 2020) and Cremon et al. (J. Comput. Phys. 418C, 2020), on large-scale thermal CO(_2) injection cases. For Carbon Capture and Sequestration (CCS) projects, injecting CO(_2) under supercritical conditions is typically tens of degrees colder than the reservoir temperature. Thermal effects can have a significant impact on the simulation results, but they also add many challenges for the solvers. More specifically, the usual combination of an iterative linear solver (such as GMRES) and the Constrained Pressure Residual (CPR) physics-based block-preconditioner is known to perform rather poorly or fail to converge when thermal effects play a significant role. The Constrained Pressure-Temperature Residual (CPTR) preconditioner retains the (2times 2) block structure (elliptic/hyperbolic) of CPR but includes the temperature in the elliptic subsystem. Doing so allows the solver to appropriately handle the long-range, elliptic part of the parabolic energy equation. The elliptic subsystem is now formed by two equations, and is dealt with by the system-solver of BoomerAMG (from the HYPRE library). Then a global smoother, ILU(0), is applied to the full system to handle the local, hyperbolic temperature fronts. We implemented CPTR in the multi-physics solver GEOS and present results on various large-scale thermal CCS simulation cases, including both Cartesian and fully unstructured meshes, up to tens of millions of degrees of freedom. The CPTR preconditioner severely reduces the number of GMRES iterations and the runtime, with cases timing out in 24h with CPR now requiring a few hours with CPTR. We present strong scaling results using hundreds of CPU cores for multiple cases, and show close to linear scaling. CPTR is also virtually insensitive to the thermal Péclet number (which compares advection and diffusion effects) and is suitable to any thermal regime.

这项工作研究了一种新型预处理器的性能,这种预处理器是为热储层模拟案例设计的,最近在 Roy 等人(SIAM J. Sci. Comput. 42, 2020)和 Cremon 等人(J. Comput. Phys. 418C, 2020)的文章中介绍了它在大规模热 CO(_2) 注入案例中的性能。对于碳捕集与封存(CCS)项目而言,在超临界条件下注入 CO(_2) 通常比储层温度低几十度。热效应会对模拟结果产生重大影响,但也会给求解器带来许多挑战。更具体地说,众所周知,迭代线性求解器(如 GMRES)和基于约束压力残余(CPR)的物理分块预处理器的常规组合在热效应起重要作用时,会表现不佳或无法收敛。约束压力-温度残差(CPTR)预处理器保留了 CPR 的 (2times 2) 块结构(椭圆/双曲),但在椭圆子系统中包含了温度。这样,求解器就能适当处理抛物能量方程的长程椭圆部分。椭圆子系统现在由两个方程组成,由 BoomerAMG(来自 HYPRE 库)的系统求解器处理。然后,全局平滑器 ILU(0) 被应用于整个系统,以处理局部双曲温度锋。我们在多物理场求解器 GEOS 中实施了 CPTR,并展示了各种大规模热 CCS 模拟案例的结果,包括笛卡尔网格和完全非结构网格,自由度高达数千万。CPTR 前处理程序大大减少了 GMRES 的迭代次数和运行时间,以前使用 CPR 时需要 24 小时,现在使用 CPTR 时只需几小时。我们在多个案例中使用数百个 CPU 内核得出了强大的扩展结果,并显示出接近线性的扩展。CPTR 对热佩克莱特数(比较平流和扩散效应)也几乎不敏感,适用于任何热环境。
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引用次数: 0
Speeding up the reservoir simulation by real time prediction of the initial guess for the Newton-Raphson’s iterations 通过实时预测牛顿-拉斐森迭代的初始猜测,加快水库模拟速度
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-09 DOI: 10.1007/s10596-024-10284-z
Musheg Petrosyants, Vladislav Trifonov, Egor Illarionov, Dmitry Koroteev

We study linear models for the prediction of the initial guess for the nonlinear Newton-Raphson solver. These models use one or more of the previous simulation steps for prediction, and their parameters are estimated by the ordinary least-squares method. A key feature of the approach is that the parameter estimation is performed using data obtained directly during the simulation and the models are updated in real time. Thus we avoid the expensive process of dataset generation and the need for pre-trained models. We validate the workflow on a standard benchmark Egg dataset of two-phase flow in porous media and compare it to standard approaches for the estimation of initial guess. We demonstrate that the proposed approach leads to reduction in the number of iterations in the Newton-Raphson algorithm and speeds up simulation time. In particular, for the Egg dataset, we obtained a 30% reduction in the number of nonlinear iterations and a 20% reduction in the simulation time.

我们研究了预测非线性牛顿-拉斐森求解器初始猜测的线性模型。这些模型使用一个或多个先前的模拟步骤进行预测,其参数用普通最小二乘法估算。这种方法的一个主要特点是,参数估计是利用在模拟过程中直接获得的数据进行的,而且模型是实时更新的。因此,我们避免了昂贵的数据集生成过程,也不需要预先训练模型。我们在多孔介质中两相流的标准基准 Egg 数据集上验证了该工作流程,并将其与估计初始猜测的标准方法进行了比较。我们证明,所提出的方法减少了牛顿-拉夫逊算法的迭代次数,加快了模拟时间。特别是在 Egg 数据集上,我们减少了 30% 的非线性迭代次数,并缩短了 20% 的模拟时间。
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引用次数: 0
A method for developing and calibrating optimization techniques for oil production management strategy applications 开发和校准石油生产管理策略应用优化技术的方法
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-08 DOI: 10.1007/s10596-024-10282-1
Leandro H. Danes, Guilherme D. Avansi, Denis J. Schiozer

The hydrocarbon extraction process is complex and involves numerous design variables and mitigating risk. Numerous time-consuming simulations are required to maximize objective functions such as NPV from a particular field while contemplating a significant representation of uncertainty scenarios and various production strategies. Production strategies searches may result in a high-dimensional search space which can yield sub-optimal reservoir economical exploration. As a solution, appropriate optimization algorithms selection and tuning may provide good solutions with lesser simulations. This paper presents a methodology to calibrate, develop, and select optimization algorithms for oil production strategy applications while quantifying the dimension and optimum location effects. Global optimum location altered the best method to be selected. It presents a novel algorithm (ASLHC) and a modification of the Nelder-Mead method (NMNS) to improve its high dimensionality performance. Performances of six pre-calibrated techniques were compared using novel normalized mathematical functions. Optimizations were limited to a 500 evaluation functions computational budget. The PSO, ASLHC, NMNS, and IDLHC were selected and implemented to perform production strategy improvements regarding two parameterizations of the reservoir management variables for a real reservoir model with restricted platform. Results showed the implemented algorithms successfully improved NPV by at least 8% at each of the 24 real-case optimizations. After upscaling the selected techniques for a 115 variable parameterization, the NMNS and IDLHC demonstrated good resilience against local convergence and each technique kept improving during all iterations of the process. An optimization method recommendation chart is presented based on the computational budget of the application.

碳氢化合物开采过程十分复杂,涉及众多设计变量和降低风险。需要进行大量耗时的模拟,以最大限度地实现目标函数,如特定油田的净现值,同时考虑大量的不确定情况和各种生产策略。生产策略搜索可能会导致高维搜索空间,从而产生次优的储层经济勘探。作为一种解决方案,选择和调整适当的优化算法可以在较少模拟的情况下提供良好的解决方案。本文介绍了一种校准、开发和选择石油生产策略应用优化算法的方法,同时量化了维度和最优位置的影响。全局最优位置改变了最佳选择方法。它提出了一种新算法(ASLHC)和对 Nelder-Mead 方法(NMNS)的修改,以提高其高维性能。使用新型归一化数学函数对六种预校准技术的性能进行了比较。优化仅限于 500 个评估函数的计算预算。选择并实施了 PSO、ASLHC、NMNS 和 IDLHC,针对一个平台受限的真实油藏模型,对油藏管理变量的两个参数化进行了生产策略改进。结果表明,所实施的算法在 24 次实际优化中,每次都成功地将净现值提高了至少 8%。在对 115 个变量参数化所选技术进行升级后,NMNS 和 IDLHC 显示出良好的抗局部收敛能力,并且每种技术在所有迭代过程中都在不断改进。根据应用的计算预算,提出了优化方法推荐图。
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引用次数: 0
Improvements in the genetic algorithm inversion of receiver functions using extinction and a new selection approach 利用消光和新的选择方法改进接收器函数的遗传算法反演
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-06 DOI: 10.1007/s10596-024-10283-0
Admore Phindani Mpuang, Takuo Shibutani

Despite the robustness of standard genetic algorithms in receiver functions inversion for crustal and uppermost mantle velocity-depth structure, one drawback is that towards the end of a ‘run’, only a few variations in solution ideas are explored. This may lead to the stagnation of the optimization process and can be a major drawback for large model dimensions. To mitigate this problem, we introduced a new selection method that retains the best features of explored models, with an extinction procedure that increases the exploration of the model space through the principle of self-organized criticality. We test the performance of the modified genetic algorithm technique by applying it to the inversion of synthetically generated receiver functions for crustal velocity structure and comparing the results with those obtained using a standard genetic algorithm. The test cases involve using 2 different objective functions, based on the L2 norm and cosine similarity, with 2 different model parameterizations of different model sizes. The results show that our modified genetic algorithm improves the inversion process by consistently obtaining best models with the lowest misfit values and a distribution of best models with less deviations from the true model values. With an improvement of computation time of up to 11.2%, the results suggest that the modified genetic algorithm is best suited to obtain higher accuracy results in shorter computation times which will be especially useful for higher dimension models needing larger pool sizes.

尽管标准遗传算法在地壳和最上层地幔速度-深度结构的接收函数反演中具有很强的鲁棒性,但它的一个缺点是,在 "运行 "即将结束时,只能探索几种不同的求解思路。这可能会导致优化过程停滞不前,对于大尺寸模型来说可能是一个主要缺点。为了缓解这一问题,我们引入了一种新的选择方法,这种方法可以保留已探索模型的最佳特征,并通过自组织临界性原理增加对模型空间的探索。我们测试了改进遗传算法技术的性能,将其用于反演合成生成的地壳速度结构接收函数,并将结果与使用标准遗传算法获得的结果进行比较。测试案例包括使用基于 L2 准则和余弦相似性的 2 个不同目标函数,以及 2 个不同模型大小的不同模型参数化。结果表明,我们改进的遗传算法能持续获得误拟合值最小的最佳模型,以及与真实模型值偏差较小的最佳模型分布,从而改进了反演过程。计算时间最多可缩短 11.2%,结果表明,改进后的遗传算法最适合在较短的计算时间内获得更高精度的结果,这对需要较大池规模的高维度模型尤其有用。
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引用次数: 0
Analysis of the hyperparameter optimisation of four machine learning satellite imagery classification methods 四种机器学习卫星图像分类方法的超参数优化分析
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-05 DOI: 10.1007/s10596-024-10285-y
Francisco Alonso-Sarría, Carmen Valdivieso-Ros, Francisco Gomariz-Castillo

The classification of land use and land cover (LULC) from remotely sensed imagery in semi-arid Mediterranean areas is a challenging task due to the fragmentation of the landscape and the diversity of spatial patterns. Recently, the use of deep learning (DL) for image analysis has increased compared to commonly used machine learning (ML) methods. This paper compares the performance of four algorithms, Random Forest (RF), Support Vector Machine (SVM), Multilayer Perceptron (MLP) and Convolutional Network (CNN), using multi-source data, applying an exhaustive optimisation process of the hyperparameters. The usual approach in the optimisation process of a LULC classification model is to keep the best model in terms of accuracy without analysing the rest of the results. In this study, we have analysed such results, discovering noteworthy patterns in a space defined by the mean and standard deviation of the validation accuracy estimated in a 10-fold cross validation (CV). The point distributions in such a space do not appear to be completely random, but show clusters of points that facilitate the discovery of hyperparameter values that tend to increase the mean accuracy and decrease its standard deviation. RF is not the most accurate model, but it is the less sensitive to changes in hyperparameters. Neural Networks, tend to increase commission and omission errors of the less represented classes because their optimisation lead the model to learn better the most frequent classes. On the other hand, RF and MLP prediction layers are the most accurate from a general qualitative point of view.

在半干旱的地中海地区,由于景观的破碎化和空间模式的多样性,从遥感图像中对土地利用和土地覆被进行分类是一项具有挑战性的任务。最近,与常用的机器学习(ML)方法相比,深度学习(DL)在图像分析中的应用越来越多。本文利用多源数据,对随机森林(RF)、支持向量机(SVM)、多层感知器(MLP)和卷积网络(CNN)这四种算法的性能进行了比较,并对超参数进行了详尽的优化。在 LULC 分类模型的优化过程中,通常的做法是保留准确率最高的模型,而不对其他结果进行分析。在本研究中,我们对这些结果进行了分析,发现了由 10 倍交叉验证(CV)中估计的验证准确率的平均值和标准偏差所定义的空间中值得注意的模式。这种空间中的点分布似乎并不是完全随机的,而是呈现出点群,有利于发现超参数值,这些超参数值往往会提高平均准确率并降低其标准偏差。射频模型并不是最准确的模型,但它对超参数变化的敏感度较低。神经网络往往会增加代表性较低类别的委托和遗漏误差,因为其优化会使模型更好地学习最常见的类别。另一方面,从一般定性的角度来看,RF 和 MLP 预测层是最准确的。
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引用次数: 0
A multi-aggregator graph neural network for backbone exaction of fracture networks 用于断裂网络骨干切除的多聚合图神经网络
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-04 DOI: 10.1007/s10596-024-10281-2
Tianji Zheng, Chengcheng Sun, Jian Zhang, Jiawei Ye, Xiaobin Rui, Zhixiao Wang

Accurately analyzing the flow and transport behavior in a large discrete fracture network is computationally expensive. Fortunately, recent research shows that most of the flow and transport occurs within a small backbone in the network, and identifying the backbone to replace the original network can greatly reduce computational consumption. However, the existing machine learning based methods mainly focus on the features of the fracture itself to evaluate the importance of the fracture, the local structural information of the fracture network is not fully utilized. More importantly, these machine learning methods can neither control the identified backbone’s size nor ensure the backbone’s connectivity. To solve these problems, a deep learning model named multi-aggregator graph neural network (MA-GNN) is proposed for identifying the backbone of discrete fracture networks. Briefly, MA-GNN uses multiple aggregators to aggregate neighbors’ structural features and thus generates an inductive embedding to evaluate the criticality score of each node in the entire fracture network. Then, a greedy algorithm, which can control the backbone’s size and connectivity, is proposed to identify the backbone based on the criticality score. Experimental results demonstrate that the backbone identified by MA-GNN can recover the transport characteristics of the original network, outperforming state-of-the-art baselines. In addition, MA-GNN can identify influential fractures with higher Kendall’s (tau ) correlation coefficient and Jaccard similarity coefficient. With the ability of size control, our proposed MA-GNN can provide an effective balance between accuracy and computational efficiency by choosing a suitable backbone size.

精确分析大型离散断裂网络中的流动和传输行为需要耗费大量计算资源。幸运的是,最近的研究表明,大部分流动和传输都发生在网络中的一个小骨干内,识别骨干来替代原始网络可以大大减少计算消耗。然而,现有的基于机器学习的方法主要关注断裂本身的特征来评估断裂的重要性,断裂网络的局部结构信息并没有得到充分利用。更重要的是,这些机器学习方法既无法控制识别出的骨干网规模,也无法确保骨干网的连通性。为了解决这些问题,我们提出了一种名为多聚合图神经网络(MA-GNN)的深度学习模型,用于识别离散断裂网络的主干网。简而言之,MA-GNN 使用多个聚合器聚合邻居的结构特征,从而生成一个归纳嵌入,以评估整个断裂网络中每个节点的临界度得分。然后,提出一种可控制骨干网大小和连通性的贪婪算法,根据临界度得分识别骨干网。实验结果表明,MA-GNN 确定的骨干网可以恢复原始网络的传输特性,性能优于最先进的基线。此外,MA-GNN 还能识别出具有较高 Kendall's (tau )相关系数和 Jaccard 相似系数的有影响力断裂。我们提出的 MA-GNN 具有大小控制能力,可以通过选择合适的骨干网大小在准确性和计算效率之间实现有效平衡。
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引用次数: 0
A mineral precipitation model based on the volume of fluid method 基于流体体积法的矿物沉淀模型
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-04-01 DOI: 10.1007/s10596-024-10280-3
Ziyan Wang, Ilenia Battiato

A novel volume of fluid method is presented for mineral precipitation coupled with fluid flow and reactive transport. The approach describes the fluid-solid interface as a smooth transitional region, which is designed to provide the same precipitation rate and viscous drag force as a sharp interface. Specifically, the governing equation of mineral precipitation is discretized by an upwind scheme, and a rigorous effective viscosity model is derived around the interface. The model is validated against analytical solutions for mineral precipitation in channel and ring-shaped structures. It also compares well with interface tracking simulations of advection-diffusion-reaction problems. The methodology is finally employed to model mineral precipitation in fracture networks, which is challenging due to the low porosity and complex geometry. Compared to other approaches, the proposed model has a concise algorithm and contains no free parameters. In the modeling, only the pore space requires meshing, which improves the computational efficiency especially for low-porosity media.

针对矿物沉淀与流体流动和反应传输的耦合,提出了一种新颖的流体体积法。该方法将流固界面描述为一个光滑的过渡区域,旨在提供与尖锐界面相同的析出率和粘性阻力。具体来说,矿物析出的控制方程采用上风方案离散化,并在界面周围推导出严格的有效粘度模型。该模型与通道和环形结构中矿物析出的分析解进行了验证。该模型还与平流-扩散-反应问题的界面跟踪模拟结果进行了比较。该方法最后被用于模拟断裂网络中的矿物沉淀,由于断裂网络孔隙率低、几何形状复杂,因此具有挑战性。与其他方法相比,所提出的模型算法简洁,不包含自由参数。在建模过程中,只需要对孔隙空间进行网格划分,从而提高了计算效率,特别是对于低孔隙率介质。
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引用次数: 0
Conditional stochastic simulation of fluvial reservoirs using multi-scale concurrent generative adversarial networks 利用多尺度并发生成式对抗网络对河流水库进行条件随机模拟
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-25 DOI: 10.1007/s10596-024-10279-w
Ting Zhang, Mengkai Yin, Hualin Bai, Anqin Zhang, Yi Du

To accurately grasp the comprehensive geological features of fluvial reservoirs, it is necessary to exploit a robust modelling approach to visualize and reproduce the realistic spatial distribution that exhibits apparent and implicit depositional trends of fluvial regions. The traditional geostatistical modelling methods using stochastic modelling fail to capture the complex features of geological reservoirs and therefore cannot reflect satisfactory realistic patterns. Generative adversarial network (GAN), as one of the mainstream generative models of deep learning, performs well in unsupervised learning tasks. The concurrent single image GAN (ConSinGAN) is one of the variants of GAN. Based on ConSinGAN, conditional concurrent single image GAN (CCSGAN) is proposed in this paper to perform conditional simulation of fluvial reservoirs, through which the output of the model can be constrained by conditional data. The results show that ConSinGAN, with the introduction of conditional data, not only preserves the model and parameters for future use but also improves the quality of the simulation results compared to other modeling methods.

为了准确把握河流储层的综合地质特征,有必要利用一种稳健的建模方法来直观地再现现实的空间分布,从而展现出河流区域明显和隐含的沉积趋势。使用随机建模的传统地质统计建模方法无法捕捉地质储层的复杂特征,因此无法反映令人满意的现实模式。生成对抗网络(GAN)作为深度学习的主流生成模型之一,在无监督学习任务中表现出色。并发单图像生成对抗网络(ConSinGAN)是生成对抗网络的变种之一。本文在 ConSinGAN 的基础上,提出了条件并发单图像 GAN(CCSGAN),用于对河流水库进行条件模拟,通过条件数据对模型的输出进行约束。结果表明,与其他建模方法相比,引入条件数据的 ConSinGAN 不仅能保留模型和参数以供将来使用,还能提高仿真结果的质量。
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引用次数: 0
A new method based on multiresolution graph-based clustering for lithofacies analysis of well logging 基于多分辨率图谱聚类的测井岩性分析新方法
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-23 DOI: 10.1007/s10596-024-10277-y

Abstract

The lithofacies analysis of logging data is an essential step in reservoir evaluation. Multiresolution graph-based clustering (MRGC) is a commonly used methodology that provides information on the best number of clusters and cluster fitting results for geological understanding. However, the cluster fusion approach of MRGC often leads to an overemphasis of the boundary constraints among clusters. MRGC neglects the global cluster distribution relationship, which limits its practical application effectiveness. This paper proposes a new methodology, named kernel multiresolution graph-based clustering (KMRGC), to improve the merging part of clustering in MRGC, and it can give more weight to the spatial relationship characteristics among clusters. The clustering performance of K-means, Gaussian Mixture Model(GMM), fuzzy c-means(FCM), Density-Based Spatial Clustering of Applications with Noise(DBSCN), spectral clustering, MRGC and KMRGC algorithm was evaluated on a publicly available training set and noisy dataset, and the best results in terms of the adjusted Rand coefficients and normalized mutual information(NMI) coefficients on most of the datasets were obtained using KMRGC algorithm. Finally, KMRGC was used for logging data lithofacies clustering in cased wells, and the clustering effect of KMRGC algorithm was much better than that of the K-means, GMM, FCM, DBSCN, spectral clustering and MRGC algorithms, and the accuracy and stability were better.

摘要 测井数据的岩性分析是储层评价的重要步骤。基于多分辨率图的聚类(MRGC)是一种常用的方法,可提供最佳聚类数量和聚类拟合结果的信息,以帮助理解地质。然而,MRGC 的聚类融合方法往往会导致过分强调聚类之间的边界约束。MRGC 忽视了全局聚类分布关系,限制了其实际应用效果。本文提出了一种新的方法,即基于核多分辨率图的聚类(KMRGC),以改进 MRGC 中的聚类合并部分,并能更多地考虑聚类间的空间关系特征。在公开的训练集和噪声数据集上评估了 K-均值、高斯混合模型(GMM)、模糊 C-均值(FCM)、基于密度的噪声应用空间聚类(DBSCN)、光谱聚类、MRGC 和 KMRGC 算法的聚类性能、结果表明,在大多数数据集上,KMRGC 算法在调整后的 Rand 系数和归一化互信息(NMI)系数方面取得了最佳结果。最后,将 KMRGC 算法用于套管井测井数据岩性聚类,KMRGC 算法的聚类效果远优于 K-means、GMM、FCM、DBSCN、光谱聚类和 MRGC 算法,且准确性和稳定性更好。
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引用次数: 0
Rigid transformations for stabilized lower dimensional space to support subsurface uncertainty quantification and interpretation 稳定低维空间的刚性变换,支持地下不确定性量化和解释
IF 2.5 3区 地球科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-03-08 DOI: 10.1007/s10596-024-10278-x
Ademide O. Mabadeje, Michael J. Pyrcz
<p>Subsurface datasets commonly are big data, i.e., they meet big data criteria, such as large data volume, significant feature variety, high sampling velocity, and limited data veracity. Large data volume is enhanced by the large number of necessary features derived from the imposition of various features derived from physical, engineering, and geological inputs, constraints that may invoke the curse of dimensionality. Existing dimensionality reduction (DR) methods are either linear or nonlinear; however, for subsurface datasets, nonlinear dimensionality reduction (NDR) methods are most applicable due to data complexity. Metric-multidimensional scaling (MDS) is a suitable NDR method that retains the data's intrinsic structure and could quantify uncertainty space. However, like other NDR methods, MDS is limited by its inability to achieve a stabilized unique solution of the low dimensional space (LDS) invariant to Euclidean transformations and has no extension for inclusions of out-of-sample points (OOSP). To support subsurface inferential workflows, it is imperative to transform these datasets into meaningful, stable representations of reduced dimensionality that permit OOSP without model recalculation.</p><p>We propose using rigid transformations to obtain a unique solution of stabilized Euclidean invariant representation for LDS. First, compute a dissimilarity matrix as the MDS input using a distance metric to obtain the LDS for <span>(N)</span>-samples and repeat for multiple realizations. Then, select the base case and perform a rigid transformation on further realizations to obtain rotation and translation matrices that enforce Euclidean transformation invariance under ensemble expectation. The expected stabilized solution identifies anchor positions using a convex hull algorithm compared to the <span>(N+1)</span> case from prior matrices to obtain a stabilized representation consisting of the OOSP. Next, the loss function and normalized stress are computed via distances between samples in the high-dimensional space and LDS to quantify and visualize distortion in a 2-D registration problem. To test our proposed workflow, a different sample size experiment is conducted for Euclidean and Manhattan distance metrics as the MDS dissimilarity matrix inputs for a synthetic dataset.</p><p>The workflow is also demonstrated using wells from the Duvernay Formation and OOSP with different petrophysical properties typically found in unconventional reservoirs to track and understand its behavior in LDS. The results show that our method is effective for NDR methods to obtain unique, repeatable, stable representations of LDS invariant to Euclidean transformations. In addition, we propose a distortion-based metric, stress ratio (SR), that quantifies and visualizes the uncertainty space for samples in subsurface datasets, which is helpful for model updating and inferential analysis for OOSP. Therefore, we recommend the workflow's integration as an invariant
地下数据集通常是大数据,即符合大数据标准,如数据量大、特征种类多、采样速度快、数据真实性有限。大数据量因大量必要特征而增强,这些特征来自于物理、工程和地质输入的各种特征,这些约束条件可能会引发维度诅咒。现有的降维(DR)方法既有线性的,也有非线性的;然而,对于地下数据集,由于数据的复杂性,非线性降维(NDR)方法最为适用。公制多维缩放(MDS)是一种合适的非线性降维方法,它保留了数据的内在结构,并能量化不确定性空间。然而,与其他 NDR 方法一样,MDS 也受到限制,因为它无法获得不受欧几里得变换影响的低维空间(LDS)的稳定唯一解,也无法扩展到包含样本外点(OOSP)。为了支持地下推断工作流程,必须将这些数据集转换为有意义的、稳定的降维表示,以便在不重新计算模型的情况下实现 OOSP。首先,使用距离度量计算一个不相似矩阵作为 MDS 输入,以获得 (N)-samples 的 LDS,并重复多次实现。然后,选择基本情况并对进一步的实现进行刚性变换,以获得在集合期望下执行欧几里得变换不变性的旋转和平移矩阵。预期稳定解使用凸壳算法确定锚点位置,并与先验矩阵的(N+1)情况进行比较,以获得由 OOSP 组成的稳定表示。接下来,通过高维空间样本间的距离和 LDS 计算损失函数和归一化应力,以量化和可视化二维配准问题中的失真。为了测试我们提出的工作流程,对合成数据集的欧几里得距离和曼哈顿距离指标作为 MDS 差异性矩阵输入进行了不同样本大小的实验。该工作流程还使用了非常规储层中具有不同岩石物理特性的 Duvernay Formation 和 OOSP 油井进行了演示,以跟踪和了解其在 LDS 中的行为。结果表明,我们的方法对于 NDR 方法来说是有效的,可以获得对欧几里得变换不变的 LDS 唯一、可重复、稳定的表示。此外,我们还提出了一种基于变形的度量--应力比(SR),该度量可量化和可视化地下数据集中样本的不确定性空间,有助于 OOSP 的模型更新和推理分析。因此,我们建议将该工作流程整合为 LDS 中的一个不变量变换缓解单元,用于独特的解决方案,以确保地下能源资源工程大数据推断工作流程(如模拟数据选择和灵敏度分析)中 NDR 方法的可重复性和合理比较。
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引用次数: 0
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Computational Geosciences
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