Inverse Approach Research Articles

Novel approaches to uncertainty estimation in seismic subsurface characterization

Uncertainty estimation in subsurface characterization workflows is an important input to decision-making in earth science-related problems. We present three methods to characterize seismic-related uncertainty, each of which includes a real data case study. Two of these methods are designed to characterize depth uncertainty in positioning of migrated reflectors. Such estimates may be used in derisking well depth prognoses, analysis of well misties, and for estimating ranges on resource volume. The first method derives rapid and robust estimates of depth uncertainty around an existing velocity model using traditional velocity analysis to constrain the solution space while limiting a-priori constraints, consistent with a frequentist approach to uncertainty characterization. The second method characterizes depth uncertainty more rigorously in respect to the physics and prior information available by performing full-waveform inversion in a Bayesian framework. This method produces similar uncertainty estimates to the first in the case of simple velocity models but is more accurate where the overburden is complex; however, it requires significantly greater computational expense, thus limiting current practical applications. The third method is an amplitude variation with angle (AVA) inversion for reservoir properties designed to output uncertainty products for interpreters, utilizing the Bayesian framework and Zoeppritz equations to define the forward physics. Application to an offshore Egypt field demonstrates that it can generate reliable estimates of reservoir properties (e.g., lithofluid type or shale volume) including uncertainty, useful in various parts of subsurface characterization. These results also show that the method could provide improved point estimates of reservoir properties compared to conventional deterministic AVA inversion approaches. There is usually a trade-off between increasing the accuracy of subsurface characterization versus creating faster, less expensive, and more readily understood workflows for practitioners. We discuss how the relative importance of these competing factors should be considered within the context of how the outputs will be used.

Nondestructively identifying the mechanical behavior of soft tissues using surface deformation with an explicit inverse approach

Identifying the spatial variation of stiffness properties in soft tissues nondestructively, with limited surface measurements, poses significant challenges. In this paper, we present a novel explicit inverse approach designed to characterize the nonhomogeneous elastic property distribution of soft tissues using only surface displacement datasets. In contrast to the prevalent implicit inverse approach, which focuses on optimizing the elastic properties of individual pixels, our proposed method optimizes the geometric parameters of deformable and movable components, as well as shear moduli of each component. As a result, the proposed approach requires far fewer optimization variables, streamlining the process. Numerical tests conducted in this study demonstrate the superiority of the explicit inverse method over the implicit inverse method, providing much-improved reconstructed results. In particular for a ring structure, while the average relative error of reconstruction using the implicit inverse method can exceed 40 %, the explicit inverse method achieves a remarkable average relative error of only 5 %. Given that surface displacements are easily measurable, the integration of our proposed explicit inverse method with low-cost imaging techniques shows great potential in accurately mapping the elastic property distribution of biological tissues.

Identification of Elastoplastic Constitutive Model of GaN Thin Films Using Instrumented Nanoindentation and Machine Learning Technique

This study presents a novel inverse identification approach to determine the elastoplastic parameters of a 2 µm thick GaN semiconductor thin film deposited on a sapphire substrate. This approach combines instrumented nanoindentation with finite element (FE) simulations and an artificial neural network (ANN) model. Experimental load–depth curves were obtained using a Berkovich indenter. To generate a comprehensive database for the inverse analysis, FE models were constructed to simulate load–depth responses across a wide range of GaN thin film properties. The accuracy of both 2D and 3D simulations was compared to select the optimal model for database generation. The Box–Behnken design-based data sampling method was used to define the number of simulations and input variables for the FE models. The ANN technique was then employed to establish the complex mapping between the simulated load–depth curves (input) and the corresponding stress–strain curve (output). The generated database was used to train and test the ANN model. Then, the learned ANN model was used to achieve high accuracy in identifying the stress–strain curve of the GaN thin film from the experimental load–depth data. This work demonstrates the successful application of an inverse analysis framework, combining experimental nanoindentation tests, FE modeling, and an ANN model, for the characterization of the elastoplastic behavior of GaN thin films.

Shape Programming of Porous Bilayer Hydrogel Structures

Abstract Shape-programmable materials have garnered significant attention for their ability to morph into complex three-dimensional (3D) configurations under external stimuli, with critical applications in the fields of biomedical engineering, soft robotics, and sensing technologies. A current challenge lies in determining the geometric parameters of the initial two-dimensional (2D) structure and the intensity of the external stimulus required to achieve a target 3D shape. In this work, we introduce a novel inverse design strategy based on hole pattern engineering. Utilizing a temperature-sensitive bilayer hydrogel with differing coefficients of thermal expansion in each layer, we achieve controlled bending deformations by varying the porosity distribution in one of the layers. Drawing on the Timoshenko theory on bimetallic beam, we establish a quantitative relationship between porosity and curvature, allowing for the hole distribution of the initial structure to be tailored to the desired curvature. We demonstrate the efficacy of our inverse design approach with several prototypical 3D structures, including variable-curvature strip and ellipsoidal surface, validated through finite element simulations and experimental trials. This strategy paves the way for advanced fabrication techniques in developing smart materials and devices with programmable shapes.

A Comparative Study of Subsurface Profile Using Bore Log Data and Geophysical Method at Mandideep Region, India

Before beginning construction on any civil structure, it is imperative to conduct a soil investigation to determine the soil’s parameters and to learn about the subsoil’s behavior. A thorough analysis must be performed, taking into account the foundation’s cost-effectiveness and any potential overdesign. In the early stages of a soil investigation, geophysical testing is used to find out about the subsurface. This is because geophysical tests are fast, easy to do, do not cause damage, and are cost-effective. In this study, subsurface profiling is performed using the inverse slope approach after resistivity tests are performed at numerous sites on varying terrain types. We generate a subsurface profile using inverse slope electrical resistivity testing and compare it with bore log data to identify any discrepancies. The results of the inverse slope method and the bore log data are comparable at different depths; further, the range of agreement of both results is determined by Bland–Altman analysis.

Next-generation membranes for verapamil removal: Graphene oxide quantum dot-modified polyethersulfone membranes

The presence of verapamil in water sources has gained attention due to its potential risks to ecosystems and human health. Because of its great separation performance and simplicity of integration into existing treatment processes, membrane filtration could be a viable alternative. Polyethersulfone (PES) membrane is usually employed for filtration processes due to its good mechanical and thermal stability. However, pristine PES membrane exhibits low flux and lower fouling properties due to its poor antibacterial properties. Thus, the phase inversion approach was used in the current study to develop graphene oxide quantum dots (GOQDs)-modified PES ultrafiltration (UF) membranes with varying quantities of GOQDs loading (0.01–0.07 wt%). With 0.03 wt% GOQDs, the PES composite membrane exhibited a water flux of 75.23 ±10.43 L/m2 h with a verapamil retention capability of 80.36%. All the modified PES membranes containing GOQDs exhibited the formation of inhibition zones, with PES-0.07 membranes (21.00 mm) showing more pronounced zones. The incorporation of GOQDs proved to be a promising and sustainable approach for modifying PES membranes, enhancing their flux, rejection performance, and antibacterial properties, which could be beneficial in removing pharmaceutical compounds from aqueous solution.

Accurate in situ rock density measurement with cosmic ray muon radiography

Muon radiography, which relies on measuring the absorption and attenuation of muons as they pass through matters, offers a new imaging technique capable of revealing the internal structure of large objects. Recent technological advancement allows for the application or testing of muon radiography in various fields, including mining, civil engineering, security check, etc. This study investigates the factors that influence muon radiography, which is used in density inversion, through simulations and experiments. The materials considered for density inversion include water, standard rock, and iron. Our simulation studies show that the number of events detected and selected has an impact on the reconstruction results, and several factors, such as multiple Coulomb scattering processes, recording time, and spatial resolution, which influence the number of muons, must be taken into account when measuring the rock density. We design and conduct a laboratory scale experiment based on the simulation results. We filter the 220 h of recording signals through time coincidence and straight-line fitting to obtain the selected events. Our results reveal that the statistical error of muons survival ratio in recording time significantly impacts the inversion result and decreases the error can improve accuracy greatly. In the experiment, the deviation between the inversion mean value and the expected value can be reduced to 2.4%–2.9% for iron, 7% for water, and 1.5% for standard rock. This density inversion approach provides insight into future density detection of underground structures.

Enhancement of filtration performance and antifouling properties of polyethersulfone membranes using Fe3O4@walnut shell-derived activated carbon nanocomposite for heavy metal ions removal

Effective water treatment methods are required owing to heavy metal ion contamination. The phase inversion approach was employed in this work to prepare antifouling polyethersulfone (PES)/Fe3O4@activated walnut shell carbon (AWSC) nanofiltration membranes to reject heavy metal ions. Characterization techniques for Fe3O4@AWSC nanoparticle (NP) included FT-IR, DLS-ZP, XRD, SEM, EDS mapping, BET, and VSM analyses. Also, SEM, EDS mapping, XRD, AFM, Zeta potential, and water contact angle investigations were utilized to characterize the synthesized membranes. The modified membranes' hydrophilicity and porosity were observed to have improved. To affirm the presence of mesoporous Fe3O4@AWSC in the membrane matrix, EDS mapping, SEM, and AFM studies were used. It was also confirmed how the membrane's characteristics and performance were influenced by the existence of mesoporous Fe3O4@AWSC. The mixed matrix membrane made of a 0.5 wt% mesoporous Fe3O4@AWSC demonstrated a high pure water flow of 72.19 L/m2 h, a flux recovery ratio of 71.66%, and a desired rejection of over 98% against Cu2+, Pb2+, and Zn2+. The 0.5 wt% NP membrane had a noticeably improved surface hydrophilicity, which promoted successful antifouling performance. The results demonstrate that a mixed-matrix antifouling Fe3O4@AWSC membrane is highly effective in eliminating heavy metal ions.

Optimising groundwater recharge to counteract seawater intrusion through an inverse modelling approach and identifying efficient recharge structure locations

In semi-arid coastal urban regions, groundwater faces challenges from seawater intrusion due to reduced recharge and increased extraction. This study employs advanced numerical modeling to comprehensively assess seawater intrusion along the South Chennai coast from 2018 to 2022. The inverse modelling approach utilizes observed data, such as groundwater heads or concentrations, to estimate aquifer properties, like hydraulic conductivity, by minimizing the disparity between model predictions and actual measurements to identify the best-fit parameter values. This inverse method forecasts the necessary recharge rate to address seawater intrusion by increasing groundwater head and decreasing chloride concentrations. The estimation of recharge incorporates variables such as rainfall, soil infiltration capacity, land use, and the vital groundwater draft calculated based on per capita consumption and population. The study uses FEFLOW software to develop a robust conceptual model, simulating groundwater flow and chloride transport. The inverse modeling approach resulted in critical recharge adjustments, enhancing rates by 40%–60% in specific regions. The predictive scenarios, integrating proposed recharge structures, show promising results, notably with a 50% reduction in chloride concentration during the post-monsoon season compared to the pre-monsoon period in wells 8 and 3. A notable decrease in chloride concentration of over 90% was observed during May 2025 in well no: 15 due to its proximity to the Adayar River. These fluctuations are influenced by seasonal variations resulting from climatic changes in South India, with intense rainfall accompanying northeast monsoon winds playing a significant role. Increased recharge rates and strategically placed structures along the Buckingham Canal provide significant relief in the most impacted northern coastal area, acting as effective barriers. These interventions successfully reduce chloride concentration, providing a sustainable and effective solution to mitigate the persistent challenge of seawater intrusion.

The lithospheric structure of Greenland from a stepwise forward and inverse modelling approach

Summary Greenland’s tectonic history is complex, and the resulting lithospheric structure is, although extensively researched, not well constrained. In this study, we model the lithospheric structure of Greenland in a consistent, integrated framework with three steps. First, we build a lithospheric background model by forward modelling, adjusted to gravity gradient data and shear wave velocities from a regional tomography model. Subsequently, we jointly invert for the upper crustal density and susceptibility structure by minimizing the gravity residuals and magnetic total field anomaly misfit. The last modelling step searches for upper crustal thermal parameters to fit our model to the most recent geothermal heat flow predictions for Greenland. Finally, we present 3D models of the density, temperature and velocity structure for the lithosphere as well as thermal parameters and susceptibilities for the upper crust. Our model also includes the depth of the Moho and LAB in Greenland. A comparison between inverted crustal parameters and surface geology shows a clear correlation. The novelty of our model is that all these results are consistent with each other and simultaneously explain a wide range of observed data.

Fingerprint recognition using convolution neural network with inversion and augmented techniques

Fingerprints are considered as one of the most important and prominent feature for an individual identification. Due to their consistency and reliability in biometric feature identification, they are most widely used for biometric recognition systems. In these systems, the relevant feature extraction plays important role in achieving required classification accuracy. In recent time, deep learning techniques are being used for fingerprint recognition with more accuracy and efficient results. Major difficulty which has been reported in previous researches, is the limited size of samples. Therefore, we propose two approaches, inversion and multi augmentation to augment the sample size with newly generated images for each feature map. Besides this, multiple networks are used simultaneously for feature extraction from newly generated images in parallel mode. Deep neural network architectures are used with proposed inversion methods and multi augmentation methods to classify the samples of fingerprints for personnel identification and verification. Pre-trained deep convolutional models like VGG16, VGG19, ResNet50 and InceptionV3 are fine-tuned with new processed fingerprint images for feature extraction and classification. The collective samples of fingerprints have been classified into 10 classes. The simulation results have been obtained with different optimizers and it has been observed that VGG 19 model exhibits the accuracies of 88 % and 93 % with inversion and multi augmentation approaches respectively. Whereas, VGG16 model exhibits 93 % with inversion approach and 97 % with multi augmentation approach. Thus, the proposed approach exhibits the accuracy up to 97 % with VGG16 model which is significantly much higher than that of any other model with the same dataset FVC2000_DB4.

Using machine learning techniques in inverse problems of acoustical oceanography

AbstractThe goal of the work presented here is to study a novel approach for inverting acoustic signals recorded in the marine environment for the estimation of environmental parameters of the water column and/or the seabed. The proposed approach is based on signal feature extraction using a discrete wavelet packet transform, applied to the measured signal, and hidden Markov models that exploit the sequential patterns of the signals. The signal feature is thereafter used in the framework of a mixture density network, which, after training with sets of simulated signals calculated within a predefined search space, provides conditional posterior distributions of the recoverable parameters. The technique is tested with two test cases corresponding to different types of inverse problems. The first case corresponds to a simple problem of geoacoustic inversion, while the second is referred to a, rather unusual, still interesting problem of recovering the shape of a seamount using long‐range acoustic data. Both test cases are based on simulated experiments. The inversion results obtained using the proposed scheme are compared with inversion results using statistical features of the acoustic signal, which is another inversion approach well documented in the literature and is also based on the wavelet packet transform of the measured signal.

Determining the Drucker-Prager Cap model constants using experimental, numerical and optimization for compacted Mg powders at different strain rates

This article investigates an inverse approach to determine the coefficients of the Drucker-Prager model for magnesium powder. The approach involves conducting finite element simulations of the powder compression process within LS-DYNA software, employing the Drucker-Prager material model. The goal is to minimize the disparity between force-displacement outcomes derived from simulations and experimental data using a surrogate optimization method. Experimental data were obtained through a uniaxial compression test and served as a basis for adjusting the Cap model coefficients. A random selection of coefficients was made using the Latin cube method and simulations were performed based on the initial coefficients. The optimization was then performed using the particle swarm algorithm over 20 iterations. The optimized coefficients were validated against experimental data, demonstrating close agreement. By utilizing the extracted coefficients, the relative density of the samples was calculated at three different compaction speeds, i.e., 15.5 m s−1 (using a Hopkinson bar), 8 m s−1 (using a drop weight), and 1 mm min−1 (using an Instron machine). The analysis revealed the highest relative density and stress in the densified sample via the Hopkinson bar method, reaching 99.83% and 1.1 GPa, respectively.

Bayesian inversion of tilt data using a machine-learned surrogate model for pressurised fractures

We introduce an innovative inversion approach for deducing subsurface fractures through observations of ground surface tilt. We have constructed, evaluated, and applied a surrogate forward model, crafted using conditional Generative Adversarial Networks (cGAN), to forecast the tilts (displacement gradients) at the ground surface caused by subsurface fractures under pressure. Our findings indicate that this surrogate forward model accurately estimates the tilt vector at the surface resulting from the specified pressurised fracture. Even in complex scenarios involving multiple fractures at various depths, the model, which was initially trained on scenarios with single fractures at a fixed depth, performed well. Subsequently, we employed a Bayesian inversion algorithm to derive the optimised solution (the pressurised fracture) for a given set of surface tilt data, leveraging the surrogate forward model. The outcomes demonstrate that the inversion process with the surrogate model is both effective and significantly faster compared to the traditional finite element model that generated the training data.

Open-source graphical user interface for the creation of synthetic skeletons for medical image analysis

Open-source graphical user interface for the creation of synthetic skeletons for medical image analysis

Substrate-Free Gas Diffusion Layer Based on a Nonsolvent-Induced Phase Inversion Approach for High-Performance Proton Exchange Membrane Fuel Cells

Substrate-Free Gas Diffusion Layer Based on a Nonsolvent-Induced Phase Inversion Approach for High-Performance Proton Exchange Membrane Fuel Cells

Optimal surface clothing with elastic nets

The clothing problem aims at identifying the shape of a planar fabric for covering a target surface in the three-dimensional space. It poses significant challenges in various applications, ranging from fashion industry to digital manufacturing. Here, we propose a novel inverse design approach to the elastic clothing problem that is formulated as a constrained optimization problem. We assume that the textile behaves as an orthotropic, nonlinear elastic surface with fibers distributed along its warp and weft threads, and we enforce mechanical equilibrium as a variational problem. The target surface is frictionless, except at its boundary where the textile is pinned, imposing a unilateral obstacle condition for the reactive forces at the target surface. The constrained optimization problem also accounts for an elongation condition of the warp and weft fibers, possibly with bounded shearing angle. We numerically solve the resulting constrained optimization problem by means of a gradient descent algorithm. The numerical results are first validated against known clothing solutions for Chebyshev nets, taking the limit of inextensible fibers. We later unravel the interplay between thread and shear stiffness for driving the optimal cloth shape covering the hemisphere and the hemicatenoid. We show how the metric of these target surfaces strongly affects the resulting distribution of the reaction forces. When considering the limit of covering the full sphere, we show how clothing with elastic nets allows to avoid the onset of singularities in the corresponding Chebyshev net, by developing corners at the cloth boundary.

Tensile behavior of polycarbonate: Key aspects for accurate constitutive modelling and simulation

Polycarbonate (PC) is a thermoplastic polymer used in many engineering applications such as safety devices and aerospace components. However, the unique behavior of PC under tensile load and its effects on the estimation of its constitutive curve are often overlooked in the literature, neglecting to consider crucial aspects of the characterization process. This work carries out a comprehensive analysis of the mechanical behavior of PC to understand the key points for accurate constitutive modeling and simulation of its static tensile performance, including its unconventional deformation mechanisms. The work starts from the accurate analysis of a representative experimental static tensile test on a rectangular section PC specimen and the evaluation of its true stress-strain curve. This analysis, carried out considering the classic length-based approach and the more accurate area-based approach, makes it possible to evaluate in detail the peculiar tensile behavior of this material. The mathematical form of the PC true stress-strain curve is then justified and the coincidence of the obtained length-based and area-based estimates of the same is demonstrated. Then, based on the in-depth understanding of the dynamics underlying the mechanical behavior of PC and making use of FEM simulations, the key points for obtaining its constitutive curve are defined. It is demonstrated that the constitutive curve is able to completely determine the behavior of PC, including its peculiar deformation mechanism. It is also highlighted which specific characteristics of the constitutive curve are critical in affecting various aspects of the material's behavior. The final constitutive curve of PC at hand is then obtained with an inverse approach, capable of accurately simulating all aspects of its tensile behavior. The validity of the proposed modelling key points is then confirmed, effectively explaining the underlying phenomena controlling the tensile behavior of PC and massively reducing uncertainty in the estimation of its constitutive curve starting from its area-based true curve.

Evaluation of inversion approaches for plates based on guided waves and modal analysis

The identification of defects in plate-like structures has been successfully treated using both local guided ultrasonic waves and global modal quantities. Although there are many papers on these techniques, a lack of comparability between the two methods persists. This makes it difficult for users to identify the most appropriate method for the defect in question. This paper examines the effect of different parameterizations of a circular defect in a square aluminum plate on the system response in a case study. The measured local ultrasound signal from a propagating guided wave makes up the initial data set. The first method uses the entire waveform for the objective function of the optimization problem, while the second considers the velocity of the A0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_0$$\\end{document} mode. In the third and fourth methods, the first and second global natural frequencies of the plate modeled with free-free boundary conditions are investigated. The numerical models are validated experimentally through measurements with a laser Doppler vibrometer. This results in the qualitative and quantitative evaluation of the objective functions for all parameter combinations of the defect. The recommendation to sequentially employ modal analysis and then the ultrasound procedure is made for the defect type used in this study. The data gathered on the objective functions suggests that potential joint employment of the natural frequency and ultrasound methods may increase computational efficiency. For a specific case, the methods could also complement each other in terms of challenges such as local minima.

Inverse modeling of frequency domain-based one-dimensional soil water flow in layered soils

Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (Ks) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of Ks everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying Ks utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between Ks and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of Ks. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of Ks. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous Ks. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK Ks is very similar to that of the VG Ks, although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK Ks can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation.