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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Recent advances in integrated hydrologic models: Integration of new domains

Over the past several decades, hydrologic models have advanced from independent models of the surface and subsurface to integrated models that can capture the terrestrial hydrologic cycle within one framework. In recent years, these coupled frameworks have seen the inclusion of biogeochemical processes, ecohydrology, sedimentation and erosion, cold region hydrology, anthropogenic activities, and atmospheric processes. This expansion is the result of increased computational, data, and modeling capabilities and capacities, as well as improved understanding of the processes that drive these integrated systems. Here, in this study, we review these recent advances to integrate new processes and systems into existing terrestrial hydrologic models and highlight the significant challenges and opportunities that remain. We identify that with so many models currently available and in development, selecting the most appropriate model is difficult, and we suggest a path for new or novice modelers to find the most appropriate code based on their needs. In addition, data required to parameterize and calibrate these models can often constrain their applicability and usefulness. However, advances in environmental sensors and measurement technology, in addition to data assimilation of non-traditional data (e.g. remote sensing, qualitative data) are providing new ways of addressing this issue. As we expand hydrologic models to integrate more processes and systems, our computational demands also increase. Recent and emerging advances in computational platforms, including cloud and quantum computing, in addition to the use of machine learning to capture some processes, will continue to support the use of increasingly larger and more complex, process-based models. Finally, we highlight that it is critical to develop state-of-the-science models that are accessible to all model users, not just those applied for research and development. We encourage continued development of diverse modeling platforms, considering the user needs, data availability, and computational resources.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems

Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

AOT_data_repo

Data repo for ocean test case testing new data assimilation algorithm in an idealized setting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Improving Tropical Cyclogenesis Forecasts of Hurricane Irma (2017) through the Assimilation of All-Sky Infrared Brightness Temperatures

The assimilation of satellite all-sky infrared (IR) brightness temperatures (BTs) has been shown in previous studies to improve intensity forecasts of tropical cyclones. Here, in this study, we examine whether assimilating all-sky IR BTs can also potentially improve tropical cyclogenesis forecasts by improving the pregenesis cloud and moisture fields. By using an ensemble-based data assimilation system, we show that the assimilation of upper-tropospheric water vapor channel BTs observed by the Meteosat-10 SEVIRI instrument two days before the formation of a tropical depression improves the genesis forecast of Hurricane Irma (2017), a classic Cape Verde storm, by up to 24 h while also capturing its later rapid intensification in deterministic forecasts. In an experiment that withholds the assimilation of all-sky IR BTs, the assimilation of conventional observations from the Global Telecommunications System (GTS) leads to the premature genesis of Hurricane Irma by at least 24 h. This premature genesis is shown to result from an overestimation of the spatial coverage of deep convection within the African easterly wave (AEW) from which Irma eventually forms. The gross overestimation of deep convection without all-sky IR BTs is accompanied by higher column saturation fraction, stronger low-level convergence, and the earlier spinup of a low-level meso- β -scale vortex within the AEW that ultimately becomes Hurricane Irma. Through its adjustment to the initial moisture and cloud conditions, the assimilation of all-sky IR BTs leads to a more realistic convective evolution in forecasts and ultimately a more realistic timing of genesis.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Assimilation of multiple datasets results in large differences in regional- to global-scale NEE and GPP budgets simulated by a terrestrial biosphere model

In spite of the importance of land ecosystems in offsetting carbon dioxide emissions released by anthropogenic activities into the atmosphere, the spatiotemporal dynamics of terrestrial carbon fluxes remain largely uncertain at regional to global scales. Over the past decade, data assimilation (DA) techniques have grown in importance for improving these fluxes simulated by terrestrial biosphere models (TBMs), by optimizing model parameter values while also pinpointing possible parameterization deficiencies. Although the joint assimilation of multiple data streams is expected to constrain a wider range of model processes, their actual benefits in terms of reduction in model uncertainty are still under-researched, also given the technical challenges. In this study, we investigated with a consistent DA framework and the ORCHIDEE-LMDz TBM–atmosphere model how the assimilation of different combinations of data streams may result in different regional to global carbon budgets. To do so, we performed comprehensive DA experiments where three datasets (in situ measurements of net carbon exchange and latent heat fluxes, spaceborne estimates of the normalized difference vegetation index, and atmospheric CO 2 concentration data measured at stations) were assimilated alone or simultaneously. We thus evaluated their complementarity and usefulness to constrain net and gross C land fluxes. We found that a major challenge in improving the spatial distribution of the land C sinks and sources with atmospheric CO 2 data relates to the correction of the soil carbon imbalance.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗
DOE OSTI2021

Leaf 13 C data constrain the uncertainty of the carbon dynamics of temperate forest ecosystems

Stable carbon isotope discrimination occurred in plant biophysical and biogeochemical processes can help understand plant physiology and soil biogeochemistry with respect to carbon cycling. Here, we incorporated the photosynthetic carbon isotope discrimination into a process-based land surface model (iTEM) to test if stable carbon isotope composition (δ 13 C) can impose additional constraint on model parameters. Sequential data assimilation was implemented at six eddy covariance flux tower sites using carbon flux observations including gross primary productivity (GPP) and net ecosystem exchange (NEE) with and without considering foliar δ 13 C (δ 13 C f ) measurement constraints, respectively. Our model-data fusion showed that δ 13 C f can provide useful constraint on photosynthetic (V cmax25 , the maximum rate of carboxylation at 25°C) and stomatal (g1, the slope of stomatal function) parameters as well as the posterior carbon fluxes. When including δ 13 C f measurement, g1 spatially varies among the six sites and is significantly correlated with annual precipitation. We incorporated the statistical relationship between g1 and annual precipitation into iTEM, which is then used to quantify the regional carbon dynamic in temperate forest ecosystems of the Northern Hemisphere. Compared with the simulation only conditioned on carbon flux observations, regional carbon flux estimations performed slightly better against the FLUXCOM products and the uncertainties of modeled carbon fluxes were reduced by 27%. Our study demonstrated that δ 13 C f data constrains carbon flux uncertainties across space.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Assimilating Scanning Radar Data into High-Resolution Models

This report documents the findings of a project aiming to improve the initial conditions of km-scale simulations of deep convective storms by assimilating cloud-scale weather radar observations. More accurate numerical analyses will increase the effectiveness of research efforts using LES cloud models as tool to better understand land-atmosphere coupling, boundary layer turbulence, and cloud processes, each used for model parameterization development. Work reported on herein includes: i) assessment of radar data sets for use in data assimilation (‘DA’) experiments, ii) quality control of the radar data set and format conversion to one acceptable to DA schemes utilized by the Weather Research and Forecasting (WRF) model, and iii) examination of the sensitivity of the numerical representation of cloud-scale wind and microphysical features to a variety of tunable DA parameters.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

The critical role of soil moisture in compound hazards

Soil moisture regulates the exchange of energy, water, and carbon across land–vegetation–atmosphere interfaces. Extremes in soil moisture can amplify natural hazards through interactions with diverse Earth system processes. Despite its mechanistic importance, soil moisture remains underrepresented in hazard research and predictive frameworks. Here, in this study, we review our current understanding of the role of soil moisture in the evolution and onset of diverse compound hazards by synthesizing the latest findings from observational and modelling studies. We highlight key soil moisture mechanisms, including atmospheric feedbacks that amplify drought–heatwave–wildfire events, precipitation couplings that promote clustered storms, and threshold responses that drive vegetation die-offs, trigger landslides, and induce flooding. Persistent challenges in observational data, model representation and operational implementation have limited the integration of soil moisture into hazard early-warning systems. Addressing these gaps through advances in observations, data assimilation, and physics-based and data-driven modelling will enhance hazard prediction and preparedness in a rapidly changing world.

Li, Chuxuan [University of California, Los Angeles↗
DOE OSTI2025

A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics

A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems –waves–, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates

This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Earth System Reanalysis in Support of Climate Model Improvements

Recent climate model developments, established through increased model resolution, have led to substantial improvements in model simulations of the time-evolving, coupled Earth system and its subcomponents. However, regardless of resolution, climate models will always produce climate features and variability that differ from the real world and will be prone to biases. This is due to many remaining uncertainties, such as in parametric and structural model uncertainty, in the initial conditions prescribed, and in the prescribed (scenario) forcing which varies on decadal to centennial timescales. Further model improvements are expected to arise specifically from improved representation of physical processes realized through model-data fusion. This will create an unprecedented opportunity to better exploit a large array of Earth observations, from in situ measurements to weather radars and satellite observations, as the resolved scales of the models approach those of the observations. For this, climate DA will be the central tool to bring models and observations into consistency, by improving initial conditions, inferring uncertain model parameters and structure, and quantifying uncertainty. Generally, there will be advantages and complementarities of adjoint-based smoother approaches, ensemble-based filter approaches, or new ML-inspired approaches. Yet, the ever-increasing model resolution will present growing challenges arising from computational cost, calling for new ways of performing data assimilation and model optimization. Using the complementarity in a hybrid approach, blending tools and concepts from variational, ensemble and ML methods might be what is required in the future. In this context ML could be important to handle non-linear responses, and to better approximate non-Gaussian distributions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks. We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. Furthermore, the DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a “plug-and-play” mode.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Measurement-driven large-eddy simulations of a diurnal cycle during a wake-steering field campaign

Abstract. High-fidelity flow modeling with data assimilation enables accurate representation of the wind farm operating environment under realistic, nonstationary atmospheric conditions. Capturing the temporal evolution of the turbulent atmospheric boundary layer is critical to understanding the behavior of wind turbines under operating conditions with simultaneously varying inflow and control inputs. This paper has three parts: the identification of a case study during a field evaluation of wake steering; the development of a tailored mesoscale-to-microscale coupling strategy that resolved local flow conditions within a large-eddy simulation (LES), using observations that did not completely capture the wind and temperature fields throughout the simulation domain; and the application of this coupling strategy to validate high-fidelity aeroelastic predictions of turbine performance and wake interactions with and without wake steering. The case study spans 4.5 h after midnight local time, during which wake steering was toggled on and off five times, achieving yaw offset angles ranging from 0 to 17°. To resolve nonstationary nighttime conditions that exhibited shear instabilities, the turbulence field was evolved starting from the diurnal cycle of the previous day. These background conditions were then used to drive wind farm simulations with two different models: an LES with actuator disk turbines and a steady-state engineering wake model. Subsequent analysis identified two representative periods during which the up- and downstream turbines were most nearly aligned with the mean wind direction and had observed yaw offsets of 0 and 15°. Both periods corresponded to partial waking on the downstream turbine, which had errors in the LES-predicted power of 4 % and 6 %, with and without wake steering. The LES was also able to capture conditions during which an upstream turbine wake induced a speedup at a downstream turbine and increased power production by up to 13 %.

17 WIND ENERGY↗
DOE OSTI2023

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗
DOE OSTI2022

Deep learning to estimate permeability using geophysical data

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.

58 GEOSCIENCES↗