Subsurface datasets inherently possess big data characteristics such as vast volume, diverse features, and high sampling speeds, further compounded by the curse of dimensionality from various physical, engineering, and geological inputs. Among the existing dimensionality reduction (DR) methods, nonlinear dimensionality reduction (NDR) methods, especially Metric-multidimensional scaling (MDS), are preferred for subsurface datasets due to their inherent complexity. While MDS retains intrinsic data structure and quantifies uncertainty, its limitations include unstabilized unique solutions invariant to Euclidean transformations and an absence of out-of-sample points (OOSP) extension. To enhance subsurface inferential and machine learning workflows, datasets must be transformed into stable, reduced-dimension representations that accommodate OOSP.
Our solution employs rigid transformations for a stabilized Euclidean invariant representation for LDS. By computing an MDS input dissimilarity matrix, and applying rigid transformations on multiple realizations, we ensure transformation invariance and integrate OOSP. This process leverages a convex hull algorithm and incorporates loss function and normalized stress for distortion quantification. We validate our approach with synthetic data, varying distance metrics, and real-world wells from the Duvernay Formation. Results confirm our method's efficacy in achieving consistent LDS representations. Furthermore, our proposed "stress ratio" (SR) metric provides insight into uncertainty, beneficial for model adjustments and inferential analysis. Consequently, our workflow promises enhanced repeatability and comparability in NDR for subsurface energy resource engineering and associated big data workflows.
College of Engineering, Peking University（北京大学工学院）；School of Environmental Science and Engineering, Southern University of Science and Technology（南方科技大学环境科学与工程学院）；Peng Cheng Laboratory（鹏城实验室）
Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty quantification for dynamic subsurface flow with a surrogate constructed by the Theory-guided Neural Network (TgNN). The TgNN here is specially designed for problems with stochastic parameters. In the TgNN, stochastic parameters, time and location comprise the input of the neural network, while the quantity of interest is the output. The neural network is trained with a…
Peng Cheng Laboratory（鹏城实验室）；Southern University of Science and Technology（南方科技大学）；Peking University（北京大学）
We build surrogate models for dynamic 3D subsurface single-phase flow problems with multiple vertical producing wells. The surrogate model provides efficient pressure estimation of the entire formation at any timestep given a stochastic permeability field, arbitrary well locations and penetration lengths, and a timestep matrix as inputs. The well production rate or bottom hole pressure can then be determined based on Peaceman's formula. The original surrogate modeling task is transformed into an image-to-image regression problem using a convolutional encoder-decoder neural network architecture…
Uncertainty quantification of two-phase flow in porous media via coupled-TgNN surrogate model
China University of Petroleum (East China)（中国石油大学（华东））；Southern University of Science and Technology（南方科技大学）；Peng Cheng Laboratory（鹏城实验室）；Peking University（北京大学）
AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flow
School of Physics and Astronomy, The University of Edinburgh（物理与天文学学院，爱丁堡大学）；Institute of GeoEnergy Engineering, School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University（地球能源工程研究所，能源、地质科学、基础设施与社会学院，赫瑞斯泰大学）；Subsurface Energy Transition and Innovation Centre, Heriot-Watt University（地下能源转型与创新中心，赫瑞斯泰大学）
SURGIN: SURrogate-guided Generative INversion for subsurface multiphase flow with quantified uncertainty
Department of Geotechnical Engineering, College of Civil Engineering, Tongji University（同济大学土木工程学院地质工程系）；Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University（教育部同济大学地质与地下工程重点实验室）；Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST)（卡布斯科学与技术大学（KAUST）物理科学与工程系）；State Key Laboratory of Marine Geology, Tongji University（同济大学海洋地质国家重点实验室）；Tencent SSV（腾讯SSV）；Tencent SD（腾讯SD）
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Colorado School of Mines（科罗拉多矿业学院）；Michigan State University（密歇根州立大学）
Monitoring changes inside a reservoir in real time is crucial for the success of CO2 injection and long-term storage. Machine learning (ML) is well-suited for real-time CO2 monitoring because of its computational efficiency. However, most existing applications of ML yield only one prediction (i.e., the expectation) for a given input, which may not properly reflect the distribution of the testing data, if it has a shift with respect to that of the training data. The Simultaneous Quantile Regression (SQR) method can estimate the entire conditional distribution of the target variable of a neural …
Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A diversity of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behavior in time. The majority of DMD algorithms, however, are prone to bias errors from noisy measurements of the dynamics, …
Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization workflows, it is common to incorporate the uncertainty of predictions thus such subsurface models should provide calibrated probabilities and the associated uncertainties in their predictions. It has been shown that popular Deep Learning-based models are often miscalibrated, and due to their deterministic nature, provide no means to interpret the uncertainty of t…
Peking University（北京大学）；Southern University of Science and Technology（南方科技大学）
A Theory-guided Auto-Encoder (TgAE) framework is proposed for surrogate construction and is further used for uncertainty quantification and inverse modeling tasks. The framework is built based on the Auto-Encoder (or Encoder-Decoder) architecture of convolutional neural network (CNN) via a theory-guided training process. In order to achieve the theory-guided training, the governing equations of the studied problems can be discretized and the finite difference scheme of the equations can be embedded into the training of CNN. The residual of the discretized governing equations as well as the dat…
Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. The heterogeneity typically requires high-fidelity physics-based models to make predictions on CO$_2$ fate. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both, heterogeneity and uncertainty, makes this a computationally-intensive problem challenging for current reservoir sim…
Machine learning for sustainable geoenergy: uncertainty, physics and decision-ready inference
Institute of GeoEnergy Engineering（地质能源工程学院）；Subsurface Energy Transition and Innovation Centre（地下能源转型与创新中心）；SubsurfaceLabs（地下实验室）；Lyell Centre（Lyell中心）
The quantification of uncertainty on fluid flow in porous media is often hampered by multi-scale heterogeneity and insufficient site characterization. Monte-Carlo simulation (MCS), which runs numerical simulations for a large number of realization of input parameters , becomes infeasible when simulation cost is expensive or the degree of uncertainty is large. Many deep-neural-network-based methods are developed in order to replace the numerical flow simulation, but previous studies focused only on generating several snapshots of outputs at the fixed time steps, and lack to reflect the time dep…
OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Rutgers University（罗格斯大学）；Michigan State University（密歇根州立大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Microsoft Research（微软研究院）
A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室）；Department of Biomedical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校生物医学工程系）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Coventry University（考文垂大学）；Malayer University（马拉耶尔大学）；Cranfield University（克兰菲尔德大学）；The University of Warwick（华威大学）
A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method is also used for reducing dimensionality of model output and consequently emulating highly complex relationship between hydrogeological properties and reduced order fluid velocity field in a tractable manner. Deep GPs are multi-layer hierarchical generalisations of GPs with multiple, infinitely wide hidden layers that are very efficient models for deep learn…
