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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems

Deep learning (DL), in particular deep neural networks, by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering problems in which underlying physical properties—such as stability, conservation, and positivity—and accuracy are required. DL methods in their original forms are often not capable of respecting the underlying mathematical models or achieving desired accuracy even in big-data regimes. On the other hand, many data-driven science and engineering problems, such as inverse problems, typically have limited experimental or observational data, and DL would overfit the data in this case. Leveraging information encoded in the underlying mathematical models, we argue, not only compensates for missing information in low data regimes but also provides opportunities to equip DL methods with the underlying physics, hence promoting better generalization. This paper develops a model-constrained DL approach and its variant TNet—a Tikhonov neural network—which are capable of learning not only information hidden in the training data but also in the underlying mathematical models to solve inverse problems governed by partial differential equations in low data regimes. We provide the constructions and some theoretical results for the proposed approaches for both linear and nonlinear inverse problems. Since TNet is designed to learn inverse solutions with Tikhonov regularization, it is interpretable: in fact it recovers Tikhonov solutions for linear cases while potentially approximating Tikhonov solutions for nonlinear inverse problems. We also prove that data randomization can enhance not only the smoothness of the networks but also their generalizations. Comprehensive numerical results confirm the theoretical findings and show that with even as little as 1 training data sample for one-dimensional (1D) deconvolution, 5 for an inverse 2D heat conductivity problem, 100 for inverse initial conditions for a time-dependent 2D Burgers’s equation, and 50 for inverse initial conditions for 2D Navier–Stokes equations, TNet solutions can be as accurate as Tikhonov solutions while being several orders of magnitude faster. Furthermore, this is possible owing to the model-constrained term, replications, and randomization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Robust Carbon Dioxide Plume Imaging Using Joint Tomographic Inversion of Seismic Onset Time and Distributed Pressure and Temperature Measurements (Final Report)

We develop and demonstrate rapid and cost-effective methodologies for spatiotemporal tracking of CO2 plumes during geologic sequestration using joint inversion of seismic data and distributed pressure and temperature measurements. Key elements of our methodology are: (a) a computationally efficient approach to pressure and temperature propagation, (b) analysis of time lapse seismic data using a novel ‘seismic onset time’ approach to detect fluid front propagation, and (c) data assimilation and uncertainty assessment via joint inversion of pressure, temperature and time lapse seismic data, and (d) validating the numerical tomographic inversion using a CO2 injection demonstration projects, specifically data collected from the from the Petra Nova Parish Holdings CCUS project in the West Ranch Field, Texas and the Chester-16 reef CO2 injection site in Northern Michigan which is part of the DOE Midwestern Carbon Sequestration Project. The research team is led by Texas A&M University and includes Battelle as a subcontractor with support from Shell, Anadarko, Chevron and JX Nippon. A carbon dioxide (CO2) water-alternating-gas (WAG) pilot was conducted to gain insights into tertiary oil recovery potential via CO2 flood in the West Ranch Field as part of the Petra Nova project, the world’s largest post-combustion CO2 capture and utilization initiative. With a fluvial formation geology and large contrasts in permeability, this is a challenging and novel application of CO2 enhanced oil recovery (EOR). We build a predictive dynamic model of the subsurface that incorporates the multiphase and compositional data acquired during the pilot operation. The calibrated model is used for the carbon dioxide plume imaging. The study began with an initialization of the pilot sector model extracted from a calibrated full-field model. The pilot model calibration follows a two-step hierarchical workflow. First, we performed a large-scale update of the permeability distribution by integrating available bottomhole pressure and multiphase production data. In the second step, local permeability field is fine-tuned using a streamline-based method to match CO2 breakthrough times at the producers. The predictive capability of the calibrated model was verified through two blind validation tests: (1) the model showed good agreement with saturation logs acquired at two observation wells; and (2) the model reproduced the CO2 recovery as a fraction of the injected CO2. The use of seismic onset times has shown great promise for integrating near-continuous seismic surveys for updating geologic models. In this study, we analyze the impact of seismic survey frequency on the onset time approach aiming to extend the application of onset time to infrequent seismic surveys. In addition, we quantitatively examine the nonlinearity of the onset time method and compare it to the commonly used amplitude inversion method. We carry out a sensitivity analysis of seismic survey frequency based on the complete seismic survey data (over 175 surveys) of steam injection in a heavy oil reservoir (Peace River Unit) in Canada. Our results show that an adequate onset time map can be obtained from the infrequent seismic surveys by interpolation between seismic surveys as long as there is no change in the dominant underlying physics between the successive surveys. The study also shows that nonlinearity of the onset time method can be -smaller than that of the amplitude inversion method by several orders of magnitude. Application to the Brugge benchmark case shows that the onset time method obtains comparable permeability update as the traditional seismic amplitude inversion method with faster computation and improved convergence characteristics. We extend the streamline-based data integration approach to incorporate distributed temperature sensor (DTS) data using the concept of thermal tracer travel time. Then, a hierarchical workflow composed of evolutionary and streamline methods is employed to jointly history match the DTS and pressure data. Finally, CO2 saturation and streamline maps are used to visualize the CO2 plume movement during the sequestration process. The hierarchical workflow is applied to a carbon sequestration project in a carbonate reef reservoir within the Northern Niagaran Pinnacle Reef Trend in Michigan, USA. The monitoring data set consists of distributed temperature sensing (DTS) data acquired at the injection well and a monitoring well, flowing bottom-hole pressure data at the injection well, and time-lapse pressure measurements at several locations along the monitoring well. The history matching results indicate that the CO2 movement is mostly restricted to the intended zones of injection which is consistent with an independent warm-back analysis of the temperature data. In addition to employing simulation models and inverse methods for CO2 plume imaging, we also initialized a data-driven technology for detecting inter-well connectivity based on production and pressure data. Our machine-learning framework is built on the statistical recurrent unit (SRU) model and interprets well-based injection/production data into inter-well connectivity without relying on a geologic model. We test it on synthetic and field-scale CO2 EOR projects utilizing the water-alternating-gas (WAG) process. The validation of the proposed data-driven inter-well connectivity assessment is performed using synthetic data from simulation models where inter-well connectivity can be easily measured using the streamline-based flux allocation. The SRU model is shown to offer excellent prediction performance on the synthetic case. Despite significant measurement noise and frequent well shut-ins imposed in the field-scale case, the SRU model offers good prediction accuracy, the overall relative error of the phase production rates at most producers ranges from 10% to 30%. It is shown that the dominant connections identified by the data-driven method and streamline method are in close agreement. Texas A&M University, the lead organization in the project, was primarily responsible for the development of tomographic approaches for CO2 plume mapping in conjunction with distributed pressure, temperature and seismic onset time data. Battelle, as a subcontractor, was primarily responsible for the development of analytical and empirical methods for analyzing transient injection rate and pressure data from point/line sources such as injection and monitoring wells. An additional area of emphasis for Battelle was the use of machine learning for such tasks as inferring reservoir connectivity information from injection-production data, and identifying variable importance for machine learning-based proxy models developed from full-physics simulations. The two organizations also collaborated on the application of the tomographic inversion methodology for a field data set.

02 PETROLEUM↗
DOE OSTI2022

A deep learning-enhanced framework for multiphysics joint inversion

Joint inversion has drawn considerable attention due to the availability of multiple geophysical data sets, ever-increasing computational resources, the development of advanced algorithms, and its ability to reduce inversion uncertainty. A key issue of joint inversion is to develop effective strategies to link different geophysical data in a unified mathematical framework, in which the information obtained from different models can complement each other. We have developed a deep learning-enhanced joint inversion framework to simultaneously reconstruct different physical models by fusing different types of geophysical data. Traditionally, structure similarity constraints are pursued by joint inversion algorithms using manually crafted formulations (e.g., cross gradient). The constraint is constructed by a deep neural network (DNN) during the learning process. The framework is designed to combine the DNN and a traditional independent inversion workflow and improve the joint inversion result iteratively. The network can be easily extended to incorporate multiphysics without structural changes. Numerical experiments on the joint inversion of 2D DC resistivity data and seismic traveltime are used to validate our method. In addition, this learning-based framework demonstrates excellent generalization abilities when tested on data sets using different geologic structures. It also can handle different sensing configurations and nonconforming discretization.

Geochemistry & Geophysics↗
DOE OSTI2024

Three-dimensional cooperative inversion of airborne magnetic and gravity gradient data using deep-learning techniques

Using multiple geophysical methods has become a prevailing approach in numerous geophysical applications to investigate subsurface structures and parameters. These multimethod-based exploration strategies have the potential to greatly diminish uncertainties and ambiguities encountered during geophysical data analysis and interpretation. One of the applications is the cooperative inversion of airborne magnetic and gravity gradient data for the interpretation of data obtained in mineral, oil and gas, and geothermal explorations. In this paper, a unified cooperative inversion framework is designed by combining the standard separate inversions with a deep neural network (DNN), which serves as the link between different types of data. A well-trained DNN takes the separately inverted susceptibility and density models as the inputs and provides improved models that will be used as the initial models of deterministic inversions. A two-round iteration strategy is adopted to guarantee the reasonability of the recovered models and overall efficiency of the inversion. In addition, this deep-learning (DL)-based framework demonstrates excellent generalization abilities when tested on models that are entirely distinct from the training data sets. The framework can easily incorporate multiphysics without necessitating any structural changes to the network. Synthetic experiments validate that our DL-based method outperforms conventional separate inversions and cross-gradient-based joint inversion in view of the accuracy of the recovered models and inversion efficiency. Successful application to field data further verifies the effectiveness of our DL-based method.

Geochemistry & Geophysics↗
NASA NTRS2015

An Inversion Analysis of Recent Variability in Natural CO2 Fluxes Using GOSAT and In Situ Observations

About one-half of the global CO2 emissions from fossil fuel combustion and deforestation accumulates in the atmosphere, where it contributes to global warming. The rest is taken up by vegetation and the ocean. The precise contribution of the two sinks, and their location and year-to-year variability are, however, not well understood. We use two different approaches, batch Bayesian synthesis inversion and variational data assimilation, to deduce the global spatiotemporal distributions of CO2 fluxes during 2009-2010. One of our objectives is to assess different sources of uncertainties in inferred fluxes, including uncertainties in prior flux estimates and observations, and differences in inversion techniques. For prior constraints, we utilize fluxes and uncertainties from the CASA-GFED model of the terrestrial biosphere and biomass burning driven by satellite observations and interannually varying meteorology. We also use measurement-based ocean flux estimates and two sets of fixed fossil CO2 emissions. Here, our inversions incorporate column CO2 measurements from the GOSAT satellite (ACOS retrieval, filtered and bias-corrected) and in situ observations (individual flask and afternoon-average continuous observations) to estimate fluxes in 108 regions over 8-day intervals for the batch inversion and at 3 x 3.75 weekly for the variational system. Relationships between fluxes and atmospheric concentrations are derived consistently for the two inversion systems using the PCTM atmospheric transport model driven by meteorology from the MERRA reanalysis. We compare the posterior fluxes and uncertainties derived using different data sets and the two inversion approaches, and evaluate the posterior atmospheric concentrations against independent data including aircraft measurements. The optimized fluxes generally resemble those from other studies. For example, the results indicate that the terrestrial biosphere is a net CO2 sink, and a GOSAT-only inversion suggests a shift in the global sink from the tropics south to the north relative to the prior and to an in-situ-only inversion. We also find a smaller terrestrial sink in higher-latitude northern regions in boreal summer of 2010 relative to 2009.

Carbon dioxide↗
NASA NTRS2017

On the Impact of Granularity of Space-Based Urban CO2 Emissions in Urban Atmospheric Inversions: A Case Study for Indianapolis, IN

Quantifying greenhouse gas (GHG) emissions from cities is a key challenge towards effective emissions management. An inversion analysis from the INdianapolis FLUX experiment (INFLUX) project, as the first of its kind, has achieved a top-down emission estimate for a single city using CO2 data collected by the dense tower network deployed across the city. However, city-level emission data, used as a priori emissions, are also a key component in the atmospheric inversion framework. Currently, fine-grained emission inventories (EIs) able to resolve GHG city emissions at high spatial resolution, are only available for few major cities across the globe. Following the INFLUX inversion case with a global 1x1 km ODIAC fossil fuel CO2 emission dataset, we further improved the ODIAC emission field and examined its utility as a prior for the city scale inversion. We disaggregated the 1x1 km ODIAC non-point source emissions using geospatial datasets such as the global road network data and satellite-data driven surface imperviousness data to a 3030 m resolution. We assessed the impact of the improved emission field on the inversion result, relative to priors in previous studies (Hestia and ODIAC). The posterior total emission estimate (5.1 MtC/yr) remains statistically similar to the previous estimate with ODIAC (5.3 MtC/yr). However, the distribution of the flux corrections was very close to those of Hestia inversion and the model-observation mismatches were significantly reduced both in forward and inverse runs, even without hourly temporal changes in emissions. EIs reported by cities often do not have estimates of spatial extents. Thus, emission disaggregation is a required step when verifying those reported emissions using atmospheric models. Our approach offers gridded emission estimates for global cities that could serves as a prior for inversion, even without locally reported EIs in a systematic way to support city-level Measuring, Reporting and Verification (MRV) practice implementation.

EIs↗
NASA NTRS2018

Affine Generalized Inverse for Optimal Control Allocation

This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set.

Acheson, Michael J.↗
NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗
DOE OSTI2022

The Influence of Temperature Inversion on the Vertical Distribution of Aerosols

Temperature inversion plays an important role in the accumulation and diffusion of aerosols. In this study, the relationship between temperature inversion and the vertical distribution of aerosols is investigated based on Raman lidar observations taken from January 2010 to September 2015 at the Atmospheric Radiation Measurement site in the Southern Great Plains, USA. First, the diurnal and seasonal variations of the surface-based inversion (SBI) and elevated temperature inversion (EI) are investigated. The results indicate that the occurrence frequency of SBI and EI have different seasonal trends. SBI has the highest frequency in summer, while EI has the highest frequency in winter. The diurnal variation of SBI is obvious, with a higher frequency in nighttime and a lower frequency in daytime. The inversion intensity (ΔT) and inversion depth (ΔZ) of SBI and EI have consistent diurnal and seasonal trends. The effects of SBI and EI on the vertical distribution of aerosols are then analyzed. The mean aerosol optical depth (AOD) below the SBI height shows a clear seasonal variation, which is consistent with the seasonal trends of ΔT and ΔZ. This phenomenon also occurs on the AOD below EI top height. The sensitivity analysis shows that the mean AOD below SBI height or EI top height increases with an increase of the ΔT and ΔZ of SBI (EI). It indicates that ΔT and ΔZ are the key factors affecting the vertical distribution of aerosols. In addition, the variation of AOD below and above EI top height is opposite to that of AOD below and above EI bottom height under different ΔT and ΔZ conditions. The correlation coefficients between ΔT (ΔZ) of EI with AOD in EI were 0.62 (0.65). These results indicate that the space between EI bottom height and EI top height can store aerosols. The larger the ΔZ of EI, the more aerosols are stored. These findings contribute to our understanding of the effect of temperature inversion on the vertical distribution of aerosols.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Generative Adversarial Networks and Mixture Density Networks-Based Inverse Modeling for Microstructural Materials Design

Abstract There are two broad modeling paradigms in scientific applications: forward and inverse. While forward modeling estimates the observations based on known causes, inverse modeling attempts to infer the causes given the observations. Inverse problems are usually more critical as well as difficult in scientific applications as they seek to explore the causes that cannot be directly observed. Inverse problems are used extensively in various scientific fields, such as geophysics, health care and materials science. Exploring the relationships from properties to microstructures is one of the inverse problems in material science. It is challenging to solve the microstructure discovery inverse problem, because it usually needs to learn a one-to-many nonlinear mapping. Given a target property, there are multiple different microstructures that exhibit the target property, and their discovery also requires significant computing time. Further, microstructure discovery becomes even more difficult because the dimension of properties (input) is much lower than that of microstructures (output). In this work, we propose a framework consisting of generative adversarial networks and mixture density networks for inverse modeling of structure–property linkages in materials, i.e., microstructure discovery for a given property. The results demonstrate that compared to baseline methods, the proposed framework can overcome the above-mentioned challenges and discover multiple promising solutions in an efficient manner.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Synthetic Evaluation of Infrasonic Multipole Waveform Inversion

Acoustic source inversions estimate the mass flow rate of volcanic explosions or yield of chemical explosions and provide insight into potential source directionality. However, the limitations of applying these methods to complex sources and their ability to resolve a stable solution have not been investigated in detail. We perform synthetic infrasound waveform inversions that use 3-D Green’s functions for a variety of idealized and realistic deployment scenarios using both a flat plane and Yasur volcano, Vanuatu as examples. We investigate the ability of various scenarios to retrieve the input source functions and relative amplitudes for monopole and multipole (monopole and dipole) inversions. Infrasound waveform inversions appear to be a robust method to quantify mass flow rates from simple sources (monopole) using deployments of infrasound sensors placed around a source, but care should be taken when analyzing and interpreting results from more complex acoustic sources (multipole) that have significant directional components. In the examples we consider the solution is stable for monopole inversions with a signal-to-noise ratio greater than five and the dipole component is small. For most scenarios investigated, the vertical dipole component of the multipole explosion source is poorly constrained and can impact the ability to recover the other source term components. Because multipole inversions are ill-posed for many deployments, a low residual does not necessarily mean the proper source vector has been recovered. Synthetic studies are able to help investigate the limitations and place bounds on information that may be missing using monopole and multipole inversions for potentially directional sources.

58 GEOSCIENCES↗
DOE OSTI2022

Diagnosing the pedestal magnetic field and magnetohydrodynamics radial structure with pedestal–scrape of layer electron cyclotron emission radiation inversion in H-mode plasma (invited)

Forward modeling is used to interpret inversion patterns of the pedestal–Scrape of Layer (SOL) Electron Cyclotron Emission (ECE) in DIII-D H-mode experiments. The modeling not only significantly improves the ECE data interpretation quality but also leads to the potential measurements of (1) the magnetic field strength |B| at the separatrix, (2) the pedestal |B| evolution during an inter-Edge Localized Mode (ELM) period, and (3) the pedestal Magnetohydrodynamics (MHD) radial structure. The ECE shine-through effect leads to three types of pedestal–SOL radiation inversions that are discussed in this paper. The first type of inversion is the non-monotonic T e,rad profile with respect to the major radius. Using the ECE frequency at the minimum T e,rad , the inversion can be applied to measure the magnetic field |B| at the separatrix and calibrate the mapping of the ECE channels with respect to the separatrix. The second type of inversion refers to the opposite phase between the radiation fluctuations δT e,rad at the pedestal and SOL. This δT e,rad phase inversion is sensitive to density and temperature fluctuations at the pedestal foot and, thus, can be used to qualitatively measure the MHD radial structure. The third type of inversion appears when the pedestal and SOL T e,rad evolve in an opposite trend, which can be used to infer the pedestal |B| field change during an inter-ELM period. Finally, the bandwidth effect on measuring δT e,rad due to pedestal MHD is also investigated in the radiation modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Bayesian Neural Network Variational Autoencoder Inverse Mapper (BNN-VAIM) and its application in Compton Form Factors extraction

Abstract We extend the Variational Autoencoder Inverse Mapper (VAIM) framework for the inverse problem of extracting Compton Form Factors (CFFs) from deeply virtual exclusive reactions, such as the unpolarized Deeply virtual exclusive scattering (DVCS) cross section. VAIM is an end-to-end deep learning framework to address the solution ambiguity issue in ill-posed inverse problems, which comprises of a forward mapper and a backward mapper to simulate the forward and inverse processes, respectively. In particular, we incorporate Bayesian Neural Network (BNN) into the VAIM architecture (BNN-VAIM) for uncertainty quantification. By sampling the weights and biases distributions of the BNN in the backward mapper of the VAIM, BNN-VAIM is able to estimate prediction uncertainty associated with each individual solution obtained for an ill-posed inverse problem. We first demonstrate the uncertainty quantification capability of BNN-VAIM in a toy inverse problem. Then, we apply BNN-VAIM to the inverse problem of extracting 8 CFFs from the unpolarized DVCS cross section.

Instruments & Instrumentation↗
DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2023

Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN

Abstract. Electrical resistivity tomography (ERT) is a broadly accepted geophysical method for subsurface investigations. Interpretation of field ERT data usually requires the application of computationally intensive forward modeling and inversion algorithms. For large-scale ERT data, the efficiency of these algorithms depends on the robustness, accuracy, and scalability on high-performance computing resources. In this regard, we present a robust and highly scalable implementation of forward modeling and inversion algorithms for ERT data. The implementation is publicly available and developed within the framework of PFLOTRAN, an open-source, state-of-the-art massively parallel subsurface flow and transport simulation code. The forward modeling is based on a finite-volume discretization of the governing differential equations, and the inversion uses a Gauss–Newton optimization scheme. To evaluate the accuracy of the forward modeling, two examples are first presented by considering layered (1D) and 3D earth conductivity models. The computed numerical results show good agreement with the analytical solutions for the layered earth model and results from a well-established code for the 3D model. Inversion of ERT data, simulated for a 3D model, is then performed to demonstrate the inversion capability by recovering the conductivity of the model. To demonstrate the parallel performance of PFLOTRAN's ERT process model and inversion capabilities, large-scale scalability tests are performed by using up to 131 072 processes on a leadership class supercomputer. These tests are performed for the two most computationally intensive steps of the ERT inversion: forward modeling and Jacobian computation. For the forward modeling, we consider models with up to 122 ×106 degrees of freedom (DOFs) in the resulting system of linear equations and demonstrate that the code exhibits almost linear scalability on up to 10 000 DOFs per process. On the other hand, the code shows superlinear scalability for the Jacobian computation, mainly because all computations are fairly evenly distributed over each process with no parallel communication.

58 GEOSCIENCES↗
NASA NTRS1992

Sources of unbounded priority inversions in real-time systems and a comparative study of possible solutions

In the design of real-time systems, tasks are often assigned priorities. Preemptive priority driven schedulers are used to schedule tasks to meet the timing requirements. Priority inversion is the term used to describe the situation when a higher priority task's execution is delayed by lower priority tasks. Priority inversion can occur when there is contention for resources among tasks of different priorities. The duration of priority inversion could be long enough to cause tasks to miss their dead lines. Priority inversion cannot be completely eliminated. However, it is important to identify sources of priority inversion and minimize the duration of priority inversion. In this paper, a comprehensive review of the problem of and solutions to unbounded priority inversion is presented.

Davari, Sadegh↗
NASA NTRS2013

Inverse Modeling of Texas NOx Emissions Using Space-Based and Ground-Based NO2 Observations

Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite observed NO2 over rural regions. Satellitebased top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with Decoupled Direct Method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2 based DKF inversion. The DKF inversions yield conflicting results: the satellite based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.

Nitrogen dioxide↗