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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2019

Three–Dimensional Acoustic Multipole Waveform Inversion at Yasur Volcano, Vanuatu

Acoustic waveform inversions can provide estimates of volume flow rate and erupted mass, enhancing the ability to estimate volcanic emissions. Previous studies have generally assumed a simple acoustic source (monopole); however, more complex and accurate source reconstructions are possible with a combination of equivalent sources (multipole). We deployed a high–density acoustic network around Yasur volcano, Vanuatu, including acoustic sensors on a tethered aerostat that was moved every ~15–60 min. Using this unique data set we invert for the acoustic multipole source mechanism using a grid search approach for 80 events to examine volume flow rates and dipole strengths. Our method utilizes finite–difference time–domain modeling to obtain the full 3–D Green's functions that account for topography. Inversion results are compared using a monopole–only, multipole (monopole and dipole), simulations that do not include topography, and those that use a subset of sensors. We find that the monopole source is a good approximation when topography is considered. However, initial compression amplitude is not fully captured by a monopole source so source directionality cannot be ruled out. The monopole solution is stable regardless of whether a monopole–only or multipole inversion is performed. Inversions for the dipole components produce estimates consistent with observed source directionality, though these inversions are somewhat unstable given station configurations of typical deployments. Furthermore, our results suggest that infrasound waveform inversion shows promise for realistic quantitative source estimates, but additional work is necessary to fully explore inversion stability, uncertainty, and robustness.

58 GEOSCIENCES↗
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 OSTI2020

A New Capability of E4D For 3D Parallel Joint Inversion of DC Resistivity And Traveltime Data on Unstructured Mesh

A major challenge in interpreting geophysical data is how to derive consistent three-dimensional (3D) earth models of different physical properties from spatially and temporally limited measurements. Joint inversion with cross-gradient constraints is an approach to find such models by imposing structural similarities between different physical parameters. We have developed a parallel distributed-memory joint inversion code for direct-current (DC) resistivity and traveltime data using the cross-gradient constraint on unstructured mesh. The code utilizes existing E4D framework for parallel forward simulation, distributed storage and computation of the Jacobian matrix of forward operator, and parallel execution of matrix-vector multiplication during inversion. Besides, the joint inversion is solved by nonlinear conjugate gradient algorithm parallelized for DC resistivity and traveltime data. The joint inversion capability of E4D was tested using synthetic data from cross-borehole DC resistivity and traveltime data. The results indicate that the shape and size of the anomalies from the joint inversion are more reliable than those from separate inversions.

58 GEOSCIENCES↗
DOE OSTI2012

Inverse Load Calculation of Wind Turbine Support Structures - A Numerical Verification Using the Comprehensive Simulation Code FAST: Preprint (Revised)

Physically measuring the dynamic responses of wind turbine support structures enables the calculation of the applied loads using an inverse procedure. In this process, inverse means deriving the inputs/forces from the outputs/responses. This paper presents results of a numerical verification of such an inverse load calculation. For this verification, the comprehensive simulation code FAST is used. FAST accounts for the coupled dynamics of wind inflow, aerodynamics, elasticity and turbine controls. Simulations are run using a 5-MW onshore wind turbine model with a tubular tower. Both the applied loads due to the instantaneous wind field and the resulting system responses are known from the simulations. Using the system responses as inputs to the inverse calculation, the applied loads arecalculated, which in this case are the rotor thrust forces. These forces are compared to the rotor thrust forces known from the FAST simulations. The results of these comparisons are presented to assess the accuracy of the inverse calculation. To study the influences of turbine controls, load cases in normal operation between cut-in and rated wind speed, near rated wind speed and between ratedand cut-out wind speed are chosen. The presented study shows that the inverse load calculation is capable of computing very good estimates of the rotor thrust. The accuracy of the inverse calculation does not depend on the control activity of the wind turbine.

17 WIND ENERGY↗
DOE OSTI2016

Inverse modeling of pan-Arctic methane emissions at high spatial resolution: what can we learn from assimilating satellite retrievals and using different process-based wetland and lake biogeochemical models?

Understanding methane emissions from the Arctic, a fast-warming carbon reservoir, is important for projecting future changes in the global methane cycle. Here we optimized methane emissions from north of 60° N (pan-Arctic) regions using a nested-grid high-resolution inverse model that assimilates both high-precision surface measurements and column-average SCanning Imaging Absorption spectroMeter for Atmospheric CHartogrphY (SCIAMACHY) satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes were integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated with six biogeochemical models. In our estimates, in 2005, global methane emissions were in the range of 496.4–511.5 Tg yr –1 , and pan-Arctic methane emissions were in the range of 11.9–28.5 Tg yr –1 . Methane emissions from pan-Arctic wetlands and lakes were 5.5–14.2 and 2.4–14.2 Tg yr –1 , respectively. Methane emissions from Siberian wetlands and lakes are the largest and also have the largest uncertainty. Our results indicate that the uncertainty introduced by different wetland models could be much larger than the uncertainty of each inversion. We also show that assimilating satellite retrievals can reduce the uncertainty of the nested-grid inversions. The significance of lake emissions cannot be identified across the pan-Arctic by high-resolution inversions, but it is possible to identify high lake emissions from some specific regions. In contrast to global inversions, high-resolution nested-grid inversions perform better in estimating near-surface methane concentrations.

58 GEOSCIENCES↗
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↗
DOE OSTI2015

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2 ) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Coupled land surface–subsurface hydrogeophysical inverse modeling to estimate soil organic carbon content and explore associated hydrological and thermal dynamics in the Arctic tundra

Quantitative characterization of soil organic carbon (OC) content is essential due to its significant impacts on surface–subsurface hydrological–thermal processes and microbial decomposition of OC, which both in turn are important for predicting carbon–climate feedbacks. While such quantification is particularly important in the vulnerable organic-rich Arctic region, it is challenging to achieve due to the general limitations of conventional core sampling and analysis methods, and to the extremely dynamic nature of hydrological–thermal processes associated with annual freeze–thaw events. In this study, we develop and test an inversion scheme that can flexibly use single or multiple datasets – including soil liquid water content, temperature and electrical resistivity tomography (ERT) data – to estimate the vertical distribution of OC content. Our approach relies on the fact that OC content strongly influences soil hydrological–thermal parameters and, therefore, indirectly controls the spatiotemporal dynamics of soil liquid water content, temperature and their correlated electrical resistivity. We employ the Community Land Model to simulate nonisothermal surface–subsurface hydrological dynamics from the bedrock to the top of canopy, with consideration of land surface processes (e.g., solar radiation balance, evapotranspiration, snow accumulation and melting) and ice–liquid water phase transitions. For inversion, we combine a deterministic and an adaptive Markov chain Monte Carlo (MCMC) optimization algorithm to estimate a posteriori distributions of desired model parameters. For hydrological–thermal-to-geophysical variable transformation, the simulated subsurface temperature, liquid water content and ice content are explicitly linked to soil electrical resistivity via petrophysical and geophysical models. We validate the developed scheme using different numerical experiments and evaluate the influence of measurement errors and benefit of joint inversion on the estimation of OC and other parameters. We also quantify the propagation of uncertainty from the estimated parameters to prediction of hydrological–thermal responses. We find that, compared to inversion of single dataset (temperature, liquid water content or apparent resistivity), joint inversion of these datasets significantly reduces parameter uncertainty. We find that the joint inversion approach is able to estimate OC and sand content within the shallow active layer (top 0.3 m of soil) with high reliability. Due to the small variations of temperature and moisture within the shallow permafrost (here at about 0.6 m depth), the approach is unable to estimate OC with confidence. However, if the soil porosity is functionally related to the OC and mineral content, which is often observed in organic-rich Arctic soil, the uncertainty of OC estimate at this depth remarkably decreases. Our study documents the value of the new surface–subsurface, deterministic–stochastic inversion approach, as well as the benefit of including multiple types of data to estimate OC and associated hydrological–thermal dynamics.

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↗
DOE OSTI2020

Bi-fidelity Gradient-Based Approach for Nonlinear Well Logging Inverse Problems

Solving a non-linear inverse problem is challenging in computational science and engineering. Sampling based methods require a large number of model valuations; gradientbased methods require fewer model evaluations but only find the local minima. Multifidelity optimization combines the low fidelity model and the high-fidelity model to achieve both high accuracy and high efficiency. In this paper, we present a bi-fidelity approach to solve non-linear inverse problems. In the bi-fidelity inversion method, the low-fidelity model is used to acquire a good initial guess, and the high-fidelity model is used to locate the global minimum. Combined with a multi-start optimization scheme, the proposed approach significantly increases the possibility of finding the global minimum for nonlinear inverse problems with many local minima. The method is tested with two toy problems and then applied to an electromagnetic well logging inverse problem, which is difficult to solve using traditional gradient-based methods. The bi-fidelity method provides promising inversion results and can be easily applied to traditional gradient-based methods.

42 ENGINEERING↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗