arXiv subjects

Louis J. Durlofsky

Publications and source records attributed to Louis J. Durlofsky.

At least 19 recordsLinked to original sources

arXiv2026

Basin-Scale Modeling of Multiple Storage Projects in the Broom Creek Formation, North Dakota, USA: Unified Model and Uncertainty Quantification

Quantifying the interactions between neighboring projects will be essential as carbon storage operations expand in scale. However, many existing basin-scale studies are deterministic or rely on hypothetical scenarios. In addition, simulations that do not fully account for neighboring projects may suffice for initial permitting. In this study, we develop a unified basin-scale model for the Broom Creek Formation in North Dakota. The model includes a total of five (existing and planned) projects, involving 18~injection wells with a maximum potential injection rate of 30~MTPA. The unified model, constructed by integrating publicly available geological and project data, contains $44\times10^6$ cells and requires over two days to run. To enable faster simulations, we present a multilevel treatment that combines four-level nested local grid refinement, constructed through the solution of a constraint-satisfaction problem, with optimized power averaging for permeability in coarse regions. After demonstrating the accuracy of the coarse model, we use it to assess uncertainty in key quantities of interest (QoIs), including total CO$_2$ injected and plume area after 50~years, across a wide range of geological realizations and model parameters. In addition, we develop a deep learning surrogate model, which is used in global sensitivity analyses to identify dominant contributors to QoI variance. Comparisons between the unified model and standalone project simulations are presented to quantify inter-project interference. This can be substantial in some cases, e.g., for one project, the median total CO$_2$ injected decreases from 271~MT (standalone) to 192~MT (unified model).

physics.geo-ph↗

arXiv2026

Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage

The use of variable well perforation and injection strategies can improve the efficiency of geological carbon storage operations. We develop a new multimodal auto-regressive transformer surrogate to model these operations under geological uncertainty. A modified SEAM CO2 geomodel, which involves a faulted system with three stacked aquifers, is considered. The two injection wells are perforated in stages, from bottom to top, with the stage durations and individual well injection rates treated as control variables. The surrogate model processes three input modalities - the 3D geomodel, scalar parameters characterizing relative permeability functions, and control variables - through separate encoders. These are fused via self-attention in a transformer encoder, and a temporal decoder generates predictions auto-regressively through encoder-decoder cross-attention. The surrogate is trained, using 4000 GEOS flow simulations, to predict saturation and pressure at monitoring locations, total injected and mobile CO2 mass, and saturation footprints. For a new test set, involving randomly sampled geomodels and control variables, the surrogate achieves a median saturation MAE of 0.028 and median relative errors of 0.2-5% for the other quantities of interest. Importantly, it captures the switch from rate to bottom-hole-pressure control. The surrogate model is used within a hierarchical Markov chain Monte Carlo data assimilation procedure for a synthetic true model under three operational strategies. Substantial uncertainty reduction is achieved for key metaparameters, particularly the fault permeabilities. Posterior predictions for saturation footprints and total injected and mobile CO2 mass are also shown to be generally consistent with true model results.

cs.LG↗

arXiv2026

Data assimilation for subsurface flow using latent diffusion model parameterization: performance of ensemble-Kalman and Monte Carlo techniques

Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism. Latent diffusion models (LDMs) provide efficient mappings from high-dimensional geological model space to a low-dimensional latent variable, reducing the dimensionality of the inverse problem while maintaining plausibility in posterior geomodels. However, the high nonlinearity in the LDM mapping may degrade the performance of Kalman-gain-based ensemble updates. We present a systematic comparison of DA algorithms applied to large-scale 3D channelized geomodels with hierarchical geological uncertainty. We compare model-space and latent-space DA using the ensemble smoother with multiple data assimilation (ESMDA), and demonstrate a key trade-off: model-space updates achieve significant uncertainty reduction but produce geologically unrealistic posterior models, while latent-space updates preserve realism but exhibit limited uncertainty reduction. Motivated by this, we explore rigorous Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) algorithms in the 3D-LDM latent space. To accommodate their high computational demands, we develop a fast surrogate flow model that approximates well-rate responses. MCMC and SMC are evaluated against ESMDA across three synthetic test cases, with DA performed in the LDM latent space. All models maintain geological realism due to the LDM parameterization. MCMC and SMC are consistent with one another and achieve lower data mismatch and more uncertainty reduction than latent-space ESMDA. Our overall results demonstrate that ensemble Kalman methods may provide overestimated posterior uncertainty with highly nonlinear parameterizations, while rigorous Monte Carlo sampling, enabled by fast surrogate models, can provide a more reliable alternative.

physics.geo-ph↗

arXiv2026

Latent diffusion models for parameterization and data assimilation of facies-based geomodels

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data assimilation (history matching), as it maintains geological realism while reducing the number of variables to be determined. Diffusion models are a new class of generative deep-learning procedures that have been shown to outperform previous methods, such as generative adversarial networks, for image generation tasks. Diffusion models are trained to "denoise", which enables them to generate new geological realizations from input fields characterized by random noise. Latent diffusion models, which are the specific variant considered in this study, provide dimension reduction through use of a low-dimensional latent variable. The model developed in this work includes a variational autoencoder for dimension reduction and a U-net for the denoising process. Our application involves conditional 2D three-facies (channel-levee-mud) systems. The latent diffusion model is shown to provide realizations that are visually consistent with samples from geomodeling software. Quantitative metrics involving spatial and flow-response statistics are evaluated, and general agreement between the diffusion-generated models and reference realizations is observed. Stability tests are performed to assess the smoothness of the parameterization method. The latent diffusion model is then used for ensemble-based data assimilation. Two synthetic "true" models are considered. Significant uncertainty reduction, posterior P$_{10}$-P$_{90}$ forecasts that generally bracket observed data, and consistent posterior geomodels, are achieved in both cases. PLEASE CITE AS: 10.1016/j.cageo.2024.105755 https://www.sciencedirect.com/science/article/pii/S0098300424002383 NOT WITH THE ARXIV VERSION

cs.CV↗

arXiv2026

3D latent diffusion models for parameterizing and history matching multiscenario facies systems

Geological parameterization procedures entail the mapping of a high-dimensional geomodel to a low-dimensional latent variable. These parameterizations can be very useful for history matching because the number of variables to be calibrated is greatly reduced, and the mapping can be constructed such that geological realism is automatically preserved. In this work, a parameterization method based on generative latent diffusion models (LDMs) is developed for 3D channel-levee-mud systems. Geomodels with variable scenario parameters, specifically mud fraction, channel orientation, and channel width, are considered. A perceptual loss term is included during training to improve geological realism. For any set of scenario parameters, an (essentially) infinite number of realizations can be generated, so our LDM parameterizes over a very wide model space. New realizations constructed using the LDM procedure are shown to closely resemble reference geomodels, both visually and in terms of one- and two-point spatial statistics. Flow response distributions, for a specified set of injection and production wells, are also shown to be in close agreement between the two sets of models. The parameterization method is applied for ensemble-based history matching, with model updates performed in the LDM latent space, for cases involving geological scenario uncertainty. For three synthetic true models corresponding to different geological scenarios, we observe clear uncertainty reduction in both production forecasts and geological scenario parameters. The overall method is additionally shown to provide posterior geomodels consistent with the synthetic true model in each case.

physics.geo-ph↗

arXiv2026

Prediction of Fault Slip Tendency in CO${_2}$ Storage using Data-space Inversion

Accurately assessing the potential for fault slip is essential in many subsurface operations. Conventional model-based history matching methods, which entail the generation of posterior geomodels calibrated to observed data, can be challenging to apply in coupled flow-geomechanics problems with faults. In this work, we implement a variational autoencoder (VAE)-based data-space inversion (DSI) framework to predict pressure, stress and strain fields, and fault slip tendency, in CO${_2}$ storage projects. The main computations required by the DSI workflow entail the simulation of O(1000) prior geomodels. The posterior distributions for quantities of interest are then inferred directly from prior simulation results and observed data, without the need to generate posterior geomodels. The model used here involves a synthetic 3D system with two faults. Realizations of heterogeneous permeability and porosity fields are generated using geostatistical software, and uncertain geomechanical and fault parameters are sampled for each realization from prior distributions. Coupled flow-geomechanics simulations for these geomodels are conducted using GEOS. A VAE with stacked convolutional long short-term memory layers is trained, using the prior simulation results, to represent pressure, strain, effective normal stress and shear stress fields in terms of latent variables. The VAE parameterization is used with DSI for posterior predictions, with monitoring wells providing observed pressure and strain data. Posterior results for synthetic true models demonstrate that the DSI-VAE framework gives accurate predictions for pressure, strain, and stress fields and for fault slip tendency. The framework is also shown to reduce uncertainty in key geomechanical and fault parameters.

cs.LG↗

arXiv2025

Bayesian Full-waveform Monitoring of CO2 Storage with Fluid-flow Priors via Generative Modeling

Quantitative monitoring of subsurface changes is essential for ensuring the safety of geological CO2 sequestration. Full-waveform monitoring (FWM) can resolve these changes at high spatial resolution, but conventional deterministic inversion lacks uncertainty quantification and incorporates only limited prior information. Deterministic approaches can also yield unreliable results with sparse and noisy seismic data. To address these limitations, we develop a Bayesian FWM framework that combines reservoir flow physics with generative prior modeling. Prior CO2 saturation realizations are constructed by performing multiphase flow simulations on prior geological realizations. Seismic velocity is related to saturation through rock physics modeling. A variational autoencoder (VAE) trained on the priors maps high-dimensional CO2 saturation fields onto a low-dimensional, approximately Gaussian latent space, enabling efficient Bayesian inference while retaining the key geometrical structure of the CO2 plume. Hamiltonian Monte Carlo (HMC) is used to infer CO2 saturation changes from time-lapse seismic data and to quantify associated uncertainties. Numerical results show that this approach improves inversion stability and accuracy under extremely sparse and noisy acquisition, whereas deterministic methods become unreliable. Statistical seismic monitoring provides posterior uncertainty estimates that identify where additional measurements would most reduce ambiguity and mitigate errors arising from biased rock physics parameters. The framework combines reservoir physics, generative priors, and Bayesian inference to provide uncertainty quantification for time-lapse monitoring of CO2 storage and other subsurface processes.

physics.geo-ph↗

arXiv2025

Recurrent Transformer U-Net Surrogate for Flow Modeling and Data Assimilation in Subsurface Formations with Faults

Many subsurface formations, including some of those under consideration for large-scale geological carbon storage, include extensive faults that can strongly impact fluid flow. In this study, we develop a new recurrent transformer U-Net surrogate model to provide very fast predictions for pressure and CO2 saturation in realistic faulted subsurface aquifer systems. The geomodel includes a target aquifer (into which supercritical CO2 is injected), surrounding regions, caprock, two extensive faults, and two overlying aquifers. The faults can act as leakage pathways between the three aquifers. The heterogeneous property fields in the target aquifer are characterized by hierarchical uncertainty, meaning both the geological metaparameters (e.g., mean and standard deviation of log-permeability) and the detailed cell properties of each realization, are uncertain. Fault permeabilities are also treated as uncertain. The model is trained with simulation results for (up to) 4000 randomly sampled realizations. Error assessments show that this model is more accurate than a previous recurrent residual U-Net, and that it maintains accuracy for qualitatively different leakage scenarios. The new surrogate is then used for global sensitivity analysis and data assimilation. A hierarchical Markov chain Monte Carlo data assimilation procedure is applied. Different monitoring strategies, corresponding to different amounts and types of observed data collected at monitoring wells, are considered for three synthetic true models. Detailed results demonstrate the degree of uncertainty reduction achieved with the various monitoring strategies. Posterior results for 3D saturation plumes and leakage volumes indicate the benefits of measuring pressure and saturation in all three aquifers.

cs.LG↗

arXiv2025

Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage

Data assimilation will be essential for the management and expansion of geological carbon storage operations. In traditional data assimilation approaches a fixed set of geological hyperparameters, such as mean and standard deviation of log-permeability, is often assumed. Such hyperparameters, however, may be highly uncertain in practical CO2 storage applications where measurements are scarce. In this study, we develop a hierarchical data assimilation framework for carbon storage that treats hyperparameters as uncertain variables characterized by hyperprior distributions. To deal with the computationally intractable likelihood function in hyperparameter estimation, we apply a likelihood-free (or simulation-based) inference algorithm, specifically sequential Monte Carlo-based approximate Bayesian computation (SMC-ABC), to draw posterior samples of hyperparameters given dynamic monitoring well data. In the second step we use an ensemble smoother with multiple data assimilation (ESMDA) procedure to provide posterior realizations of grid-block permeability. To reduce computational costs, a 3D recurrent R-U-Net deep learning-based surrogate model is applied for forward function evaluations. A rejection sampling (RS) procedure for data assimilation is applied to provide reference posterior results. Detailed posterior results from SMC-ABC-ESMDA are compared to those from the reference RS method. Close agreement is achieved with 'converged' RS results, for two synthetic true models, in all quantities considered. Importantly, the SMC-ABC-ESMDA procedure provides speedup of 1-2 orders of magnitude relative to RS for the two cases. A modified standalone ESMDA procedure is introduced for comparison purposes. For the same number of function evaluations, the hierarchical approach is shown to provide superior results for posterior hyperparameter distributions and monitoring well pressure predictions.

cs.LG↗

arXiv2025

Deep Learning Framework for History Matching CO2 Storage with 4D Seismic and Monitoring Well Data

Geological carbon storage entails the injection of megatonnes of supercritical CO2 into subsurface formations. The properties of these formations are usually highly uncertain, which makes design and optimization of large-scale storage operations challenging. In this paper we introduce a history matching strategy that enables the calibration of formation properties based on early-time observations. Early-time assessments are essential to assure the operation is performing as planned. Our framework involves two fit-for-purpose deep learning surrogate models that provide predictions for in-situ monitoring well data and interpreted time-lapse (4D) seismic saturation data. These two types of data are at very different scales of resolution, so it is appropriate to construct separate, specialized deep learning networks for their prediction. This approach results in a workflow that is more straightforward to design and more efficient to train than a single surrogate that provides global high-fidelity predictions. The deep learning models are integrated into a hierarchical Markov chain Monte Carlo (MCMC) history matching procedure. History matching is performed on a synthetic case with and without 4D seismic data, which allows us to quantify the impact of 4D seismic on uncertainty reduction. The use of both data types is shown to provide substantial uncertainty reduction in key geomodel parameters and to enable accurate predictions of CO2 plume dynamics. The overall history matching framework developed in this study represents an efficient way to integrate multiple data types and to assess the impact of each on uncertainty reduction and performance predictions.

cs.LG↗

arXiv2024

Graph Network Surrogate Model for Optimizing the Placement of Horizontal Injection Wells for CO2 Storage

Optimizing the locations of multiple CO2 injection wells will be essential as we proceed from demonstration-scale to large-scale carbon storage operations. Well placement optimization is, however, a computationally intensive task because the flow responses associated with many potential configurations must be evaluated. There is thus a need for efficient surrogate models for this application. In this work we develop and apply a graph network surrogate model (GNSM) to predict the global pressure and CO2 saturation fields in 3D geological models for arbitrary configurations of four horizontal wells. The GNSM uses an encoding-processing-decoding framework where the problem is represented in terms of computational graphs. Separate networks are applied for pressure and saturation predictions, and a multilayer perceptron is used to provide bottom-hole pressure (BHP) for each well at each time step. The GNSM is shown to achieve median relative errors of 4\% for pressure and 6\% for saturation over a test set involving very different plume shapes and dynamics. Speedup is about a factor of $120\times$ relative to high-fidelity simulation. The GNSM is applied for optimization using a differential evolution algorithm, where the goal is to minimize the CO2 footprint subject to constraints on the well configuration, plume location and well BHPs. Optimization results using the GNSM are shown to be comparable to those achieved using (much more expensive) high-fidelity simulation.

cs.CE↗

arXiv2024

Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations

Deep learning surrogate modeling shows great promise for subsurface flow applications, but the training demands can be substantial. Here we introduce a new surrogate modeling framework to predict CO2 saturation, pressure and surface displacement for use in the history matching of carbon storage operations. Rather than train using a large number of expensive coupled flow-geomechanics simulation runs, training here involves a large number of inexpensive flow-only simulations combined with a much smaller number of coupled runs. The flow-only runs use an effective rock compressibility, which is shown to provide accurate predictions for saturation and pressure for our system. A recurrent residual U-Net architecture is applied for the saturation and pressure surrogate models, while a new residual U-Net model is introduced to predict surface displacement. The surface displacement surrogate accepts, as inputs, geomodel quantities along with saturation and pressure surrogate predictions. Median relative error for a diverse test set is less than 4% for all variables. The surrogate models are incorporated into a hierarchical Markov chain Monte Carlo history matching workflow. Surrogate error is included using a new treatment involving the full model error covariance matrix. A high degree of prior uncertainty, with geomodels characterized by uncertain geological scenario parameters (metaparameters) and associated realizations, is considered. History matching results for a synthetic true model are generated using in-situ monitoring-well data only, surface displacement data only, and both data types. The enhanced uncertainty reduction achieved with both data types is quantified. Posterior saturation and surface displacement fields are shown to correspond well with the true solution.

cs.LG↗

arXiv2024

Graph Network Surrogate Model for Subsurface Flow Optimization

The optimization of well locations and controls is an important step in the design of subsurface flow operations such as oil production or geological CO2 storage. These optimization problems can be computationally expensive, however, as many potential candidate solutions must be evaluated. In this study, we propose a graph network surrogate model (GNSM) for optimizing well placement and controls. The GNSM transforms the flow model into a computational graph that involves an encoding-processing-decoding architecture. Separate networks are constructed to provide global predictions for the pressure and saturation state variables. Model performance is enhanced through the inclusion of the single-phase steady-state pressure solution as a feature. A multistage multistep strategy is used for training. The trained GNSM is applied to predict flow responses in a 2D unstructured model of a channelized reservoir. Results are presented for a large set of test cases, in which five injection wells and five production wells are placed randomly throughout the model, with a random control variable (bottom-hole pressure) assigned to each well. Median relative error in pressure and saturation for 300 such test cases is 1-2%. The ability of the trained GNSM to provide accurate predictions for a new (geologically similar) permeability realization is demonstrated. Finally, the trained GNSM is used to optimize well locations and controls with a differential evolution algorithm. GNSM-based optimization results are comparable to those from simulation-based optimization, with a runtime speedup of a factor of 36. Much larger speedups are expected if the method is used for robust optimization, in which each candidate solution is evaluated on multiple geological models.

physics.geo-ph↗

arXiv2024

Surrogate Model for Geological CO2 Storage and Its Use in Hierarchical MCMC History Matching

Deep-learning-based surrogate models show great promise for use in geological carbon storage operations. In this work we target an important application - the history matching of storage systems characterized by a high degree of (prior) geological uncertainty. Toward this goal, we extend the recently introduced recurrent R-U-Net surrogate model to treat geomodel realizations drawn from a wide range of geological scenarios. These scenarios are defined by a set of metaparameters, which include the horizontal correlation length, mean and standard deviation of log-permeability, permeability anisotropy ratio, and constants in the porosity-permeability relationship. An infinite number of realizations can be generated for each set of metaparameters, so the range of prior uncertainty is large. The surrogate model is trained with flow simulation results, generated using the open-source simulator GEOS, for 2000 random realizations. The flow problems involve four wells, each injecting 1 Mt CO2/year, for 30 years. The trained surrogate model is shown to provide accurate predictions for new realizations over the full range of geological scenarios, with median relative error of 1.3% in pressure and 4.5% in saturation. The surrogate model is incorporated into a hierarchical Markov chain Monte Carlo history matching workflow, where the goal is to generate history matched geomodel realizations and posterior estimates of the metaparameters. We show that, using observed data from monitoring wells in synthetic `true' models, geological uncertainty is reduced substantially. This leads to posterior 3D pressure and saturation fields that display much closer agreement with the true-model responses than do prior predictions.

cs.CV↗

arXiv2023

History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization

History matching based on monitoring data will enable uncertainty reduction, and thus improved aquifer management, in industrial-scale carbon storage operations. In traditional model-based data assimilation, geomodel parameters are modified to force agreement between flow simulation results and observations. In data-space inversion (DSI), history-matched quantities of interest, e.g., posterior pressure and saturation fields conditioned to observations, are inferred directly, without constructing posterior geomodels. This is accomplished efficiently using a set of O(1000) prior simulation results, data parameterization, and posterior sampling within a Bayesian setting. In this study, we develop and implement (in DSI) a deep-learning-based parameterization to represent spatio-temporal pressure and CO2 saturation fields at a set of time steps. The new parameterization uses an adversarial autoencoder (AAE) for dimension reduction and a convolutional long short-term memory (convLSTM) network to represent the spatial distribution and temporal evolution of the pressure and saturation fields. This parameterization is used with an ensemble smoother with multiple data assimilation (ESMDA) in the DSI framework to enable posterior predictions. A realistic 3D system characterized by prior geological realizations drawn from a range of geological scenarios is considered. A local grid refinement procedure is introduced to estimate the error covariance term that appears in the history matching formulation. Extensive history matching results are presented for various quantities, for multiple synthetic true models. Substantial uncertainty reduction in posterior pressure and saturation fields is achieved in all cases. The framework is applied to efficiently provide posterior predictions for a range of error covariance specifications. Such an assessment would be expensive using a model-based approach.

cs.LG↗

arXiv2022

Multi-Asset Closed-Loop Reservoir Management Using Deep Reinforcement Learning

Closed-loop reservoir management (CLRM), in which history matching and production optimization are performed multiple times over the life of an asset, can provide significant improvement in the specified objective. These procedures are computationally expensive due to the large number of flow simulations required for data assimilation and optimization. Existing CLRM procedures are applied asset by asset, without utilizing information that could be useful over a range assets. Here, we develop a CLRM framework for multiple assets with varying numbers of wells. We use deep reinforcement learning to train a single global control policy that is applicable for all assets considered. The new framework is an extension of a recently introduced control policy methodology for individual assets. Embedding layers are incorporated into the representation to handle the different numbers of decision variables that arise for the different assets. Because the global control policy learns a unified representation of useful features from multiple assets, it is less expensive to construct than asset-by-asset training (we observe about 3x speedup in our examples). The production optimization problem includes a relative-change constraint on the well settings, which renders the results suitable for practical use. We apply the multi-asset CLRM framework to 2D and 3D water-flooding examples. In both cases, four assets with different well counts, well configurations, and geostatistical descriptions are considered. Numerical experiments demonstrate that the global control policy provides objective function values, for both the 2D and 3D cases, that are nearly identical to those from control policies trained individually for each asset. This promising finding suggests that multi-asset CLRM may indeed represent a viable practical strategy.

cs.LG↗

arXiv2022

Convolutional-Recurrent Neural Network Proxy for Robust Optimization and Closed-Loop Reservoir Management

Production optimization under geological uncertainty is computationally expensive, as a large number of well control schedules must be evaluated over multiple geological realizations. In this work, a convolutional-recurrent neural network (CNN-RNN) proxy model is developed to predict well-by-well oil and water rates, for given time-varying well bottom-hole pressure (BHP) schedules, for each realization in an ensemble. This capability enables the estimation of the objective function and nonlinear constraint values required for robust optimization. The proxy model represents an extension of a recently developed long short-term memory (LSTM) RNN proxy designed to predict well rates for a single geomodel. A CNN is introduced here to processes permeability realizations, and this provides the initial states for the RNN. The CNN-RNN proxy is trained using simulation results for 300 different sets of BHP schedules and permeability realizations. We demonstrate proxy accuracy for oil-water flow through multiple realizations of 3D multi-Gaussian permeability models. The proxy is then incorporated into a closed-loop reservoir management (CLRM) workflow, where it is used with particle swarm optimization and a filter-based method for nonlinear constraint satisfaction. History matching is achieved using an adjoint-gradient-based procedure. The proxy model is shown to perform well in this setting for five different (synthetic) `true' models. Improved net present value along with constraint satisfaction and uncertainty reduction are observed with CLRM. For the robust production optimization steps, the proxy provides O(100) runtime speedup over simulation-based optimization.

cs.LG↗

arXiv2022

Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Models

Data assimilation presents computational challenges because many high-fidelity models must be simulated. Various deep-learning-based surrogate modeling techniques have been developed to reduce the simulation costs associated with these applications. However, to construct data-driven surrogate models, several thousand high-fidelity simulation runs may be required to provide training samples, and these computations can make training prohibitively expensive. To address this issue, in this work we present a framework where most of the training simulations are performed on coarsened geomodels. These models are constructed using a flow-based upscaling method. The framework entails the use of a transfer-learning procedure, incorporated within an existing recurrent residual U-Net architecture, in which network training is accomplished in three steps. In the first step. where the bulk of the training is performed, only low-fidelity simulation results are used. The second and third steps, in which the output layer is trained and the overall network is fine-tuned, require a relatively small number of high-fidelity simulations. Here we use 2500 low-fidelity runs and 200 high-fidelity runs, which leads to about a 90% reduction in training simulation costs. The method is applied for two-phase subsurface flow in 3D channelized systems, with flow driven by wells. The surrogate model trained with multifidelity data is shown to be nearly as accurate as a reference surrogate trained with only high-fidelity data in predicting dynamic pressure and saturation fields in new geomodels. Importantly, the network provides results that are significantly more accurate than the low-fidelity simulations used for most of the training. The multifidelity surrogate is also applied for history matching using an ensemble-based procedure, where accuracy relative to reference results is again demonstrated.

cs.LG↗