Inverse Method Research Articles

VILLAGE APPARATUS PERFORMANCE: THE ROLE OF CULTURE, ORGANIZATION SUPPORT AND JOB SATISFACTION?

The performance of village officials has always been a focal point for various parties because the foundation of urban and national progress lies in rural development. However, the performance of village officials in Indonesia is still not optimal. This study aims to investigate the roles of job satisfaction, organizational culture, and perceived organizational support as mediators and moderators in the relationship between competence and performance. The research involved 368 village officials across 19 regencies in West Java province, selected using the inverse root square method. Data collection was conducted through questionnaire distribution using area random sampling methods. Data analysis was performed using Warp PLS method. The findings indicate that job satisfaction successfully mediates the relationship between competence and performance. Organizational culture and perceived organizational support significantly moderate the influence of competence on performance. Village government bodies, village community empowerment agencies, and the Ministry of Villages need to formulate policies that support improving job satisfaction, foster a healthy organizational culture, and provide facilitative support, both in infrastructure and in developing hard and soft skills for village officials.

Estimation of electrical conductivity models using multi-coil rigid-boom electromagnetic induction measurements

Electromagnetic induction measurements from multi-coil configuration instruments are used to obtain information about the electrical conductivity distribution in the subsurface. The resulting inverse problem might not have a unique and stable solution. In that case, a local inversion method can be trapped in a local minimum and lead to an incorrect solution. In this study, we evaluate the well-posedness of the inverse problem for two and three-layered electrical conductivity models. We show that for a two-layered model, uniqueness is ensured only when both in-phase and quadrature data are available from the measurements. Results from a Gauss–Newton inversion and a lookup table demonstrate that the solution space is convex. Furthermore, we demonstrate that for even a simple three-layered model, the data contained in such measurements are insufficient to reach a correct or stable solution. For models with more than 2 layers, independent prior information is necessary to solve the inverse problem. The insights from the numerical examples are applied in a field case.

The linear swept sine method to determine the dispersion curve of structural pavement

Abstract Pavement evaluation must be performed in nondestructive ways. This includes using the multichannel analysis of surface waves method by recording waves detected by multiple sensors from one active source. However, heavy traffic produces noise and reduces the detection quality as the sensor moves further away from the measurement source. We need a pavement evaluation method that is immune to noise. The linear swept-sine method presented in this paper has a very high resistance to noise by using a wide frequency band vibration source to the ground received by a single accelerometer at a small distance. The noise resistance is obtained by applying a tracking filter at the receiver (accelerometer), which accepts the signal with the frequency swept linearly at the same rate as the transmitter. This tracking filter has a low-frequency component equal to the phase delay between the source and the receiver, even when the transmitted source is generated in the high-frequency range. The dispersion curve is calculated and inverted by using the surface wave inversion method to obtain the velocity model below the pavement by calculating the delay for each data segment.

Fast inverse design of microwave and infrared Bi-stealth metamaterials based on equivalent circuit model

This work proposed a fast inverse design method for microwave and infrared (IR) bi-stealth metamaterials based on the equivalent circuit model (ECM). Using this method, we designed a microwave and IR bi-stealth metamaterial by deploying a multilayered structure of the indium tin oxide (ITO) film based metasurface. First, the IR emissivity of the ITO film was calculated in the framework of the ECM. Then, an ITO metasurface was proposed to implement low IR emission and high microwave transmission simultaneously. Based on the ECM of the square patch, the ECM of the whole metamaterial was established at the microwave band. An inverse design program was built by incorporating the ECM with genetic algorithm (GA). Structure parameters of the metamaterial were optimized by GA to achieve the broadest microwave stealth bandwidth for the given thickness. Finally, the sample of the optimized bi-stealth metamaterial was prepared and tested. The calculated, simulated, and measured results are in good agreement, showing that such a metamaterial has an IR emissivity of 0.18 in the band from 3 to 14 μm and an efficient microwave stealth band from 4.8 to 17 GHz with a thickness of 4.9 mm. The proposed method will benefit the design and application of microwave and IR bi-stealth metamaterials.

Inverse design of cellular structures with the geometry of triply periodic minimal surfaces using generative artificial intelligence algorithms

Triply periodic minimal surfaces (TPMS) exhibit excellent mechanical and energy absorption properties due to their structural advantages. However, existing porous TPMS structural design methods are constrained to a forward process from structural parameters to mechanical properties. This study proposed an inverse design method that combines bidirectional generative adversarial networks (BiGAN) and mechanical performance targets, resulting in a combined TPMS structure of Primitive and IWP types with superior buffering and energy absorption capabilities. The results show that under a single load value target condition of the designed structure, the minimum deviation index (R2) between the load value corresponding to the displacement point and the target load value is only 0.987, and the maximum mean absolute percentage error (MAPE) is only 5.92 %. When considering the elastic modulus target, the approach successfully conducts two sets of combined structural designs meeting the requirements of both high and low elastic moduli. When targeting the specified load-displacement curve conditions, specifically when combining high elastic modulus with ascending plasticity, the designed structures exhibit an error of only 2.2 % compared to the target property. Moreover, the quasi-static uniaxial compression experiments conducted on additively manufactured designed structures confirm that the experimental curves match the target curves in terms of deformation trends and load value ranges. The success of this inverse design approach for cellular TPMS structures has the potential to expedite new structural material development processes.

Inverse Estimation of Swirl Cooling Heat Transfer Coefficient

Swirl cooling is one of the most widely studied techniques in the field of heat transfer enhancement. This paper presents a novel, non-intrusive, and rather inexpensive inverse method to estimate the local heat transfer coefficient along the swirl chamber. First, the direct problem of two-dimensional heat conduction inside the chamber’s wall is solved numerically. The optimal number of sensors, their axial and radial positions, and other parameters concerning the inverse algorithm are determined using simulated experiments. The experimental setup is built based on these parameters. Transient temperature readings from several thermocouples embedded inside the chamber wall are fed to an inverse algorithm based on the conjugate gradient method. This algorithm takes advantage of an adjoint differential equation and the sensitivity differential equation to calculate the gradients and optimal step sizes, respectively. The local transient heat transfer coefficient is estimated for three Reynolds numbers along four straight lines parallel to the axis of the chamber.

Forest Canopy Height Estimation Combining Dual-Polarization PolSAR and Spaceborne LiDAR Data

Forest canopy height data are fundamental parameters of forest structure and are critical for understanding terrestrial carbon stock, global carbon cycle dynamics and forest productivity. To address the limitations of retrieving forest canopy height using conventional PolInSAR-based methods, we proposed a method to estimate forest height by combining single-temporal polarimetric synthetic aperture radar (PolSAR) images with sparse spaceborne LiDAR (forest height) measurements. The core idea of our method is that volume scattering energy variations which are linked to forest canopy height occur during radar acquisition. Specifically, our methodology begins by employing a semi-empirical inversion model directly derived from the random volume over ground (RVoG) formulation to establish the relationship between forest canopy height, volume scattering energy and wave extinction. Subsequently, PolSAR decomposition techniques are used to extract canopy volume scattering energy. Additionally, machine learning is employed to generate a spatially continuous extinction coefficient product, utilizing sparse LiDAR samples for assistance. Finally, with the derived inversion model and the resulting model parameters (i.e., volume scattering power and extinction coefficient), forest canopy height can be estimated. The performance of the proposed forest height inversion method is illustrated with L-band NASA/JPL UAVSAR from AfriSAR data conducted over the Gabon Lope National Park and airborne LiDAR data. Compared to high-accuracy airborne LiDAR data, the obtained forest canopy height from the proposed approach exhibited higher accuracy (R2 = 0.92, RMSE = 6.09 m). The results demonstrate the potential and merit of the synergistic combination of PolSAR (volume scattering power) and sparse LiDAR (forest height) measurements for forest height estimation. Additionally, our approach achieves good performance in forest height estimation, with accuracy comparable to that of the multi-baseline PolInSAR-based inversion method (RMSE = 5.80 m), surpassing traditional PolSAR-based methods with an accuracy of 10.86 m. Given the simplicity and efficiency of the proposed method, it has the potential for large-scale forest height estimation applications when only single-temporal dual-polarization acquisitions are available.

Inverse design of metamaterial for dual-band infrared camouflage along with dual-band thermal management

The optical metamaterial for infrared camouflage with thermal management is an artificial structure available to not only evade the detection of various thermal imagers operating in distinct infrared wavebands but also ensure the thermal stability of the target. However, designing such an optical metamaterial is challenging due to the necessity to optimize numerous structural parameters simultaneously, especially metamaterials that are compatible with multiple functions. Herein, this paper proposes a novel inverse design method, combining African vultures optimization algorithm (AVOA) with rigorous coupled-wave analysis (RCWA), to design an optical metamaterial capable of achieving infrared camouflage and thermal management compatibly. The proposed metamaterial enables dual-band infrared camouflage for mid-wave infrared (MWIR, 3–5 μm) and long-wave infrared (LWIR, 8–14 μm), along with thermal management through dual-band non-atmospheric windows of 5–8 μm and 14–17 μm. Comparing to other intelligent optimization algorithms, the AVOA is exceptionally efficient, which only takes less time than others to get better results. This work not only provides theoretical guidance to design an optical metamaterial for infrared camouflage with thermal management, but also has the potential to solve the multi-objective optimization problems of multi-band or wide-band radiative modulation.

Preparation and performance characterization of waterborne epoxy resin modified asphalt emulsion for tack coat

In order to eliminate the possible drawbacks of waterborne epoxy resin (WER) generated by the phase inversion method and the chemical modification method, this study prepared WER using a novel method, i.e., epoxy resin was introduced into the molecular structure of aqueous acrylic resin; after the combination of epoxy resin and the aqueous dispersion process, the aqueous epoxy acrylic resin can be prepared. Waterborne epoxy resin modified emulsified asphalt (WEREA) was then prepared for the application of a tack coat material. Fourier Transform Infrared Spectroscopy (FTIR) test was conducted to explore the possible reactions between the compositions. A rheology test, direct tension test, pull-off bonding test, and oblique shear test were also conducted. Results indicated that in the FTIR test, a new peak around 1732 cm−1 was formed due to the reaction between the carboxyl functional group in WER and the amino group in curing agent to form an ester bond. The incorporation of WER led to an elevation in the complex modulus and a simultaneous reduction in the phase angle of WEREA. When the temperature was larger than 60 °C, the phase angle showed a decreased trend, indicating the material became less viscous due to the increased temperature, illustrating thermosetting characteristics of epoxy resin. As the content of waterborne epoxy resin (WER) increased, there was an observed decrease in the direct tensile rate, coupled with a concurrent increase in direct tensile strength. When the ratio of emulsified asphalt and WER was 1:0.6, the tensile strength of WEREA increased by 811% in contrast to the specimen without the inclusion of WER. There existed different optimal WER contents for the pull-off strength tests conducted on different substrates. For asphalt concrete substrate and steel slab substrate, the optimum ratio of emulsified asphalt to WER + curing agent was 1:0.4, and 1:0.8 was the optimum ratio for the cement concrete substrate. When the ratio between emulsified asphalt and the combination of WER along with the curing agent was 1:0.4 (WEREA-4), the oblique shear strength obtained the maximum value, which was increased by 18.7% in contrast to WEREA-0.

Splitting intensity tomography to image depth-dependent seismic anisotropy patterns beneath the Italian Peninsula and surrounding regions

The region between central Europe and the centre of the Mediterranean is characterised by complex tectonics and kinematics. Here, the interaction between thickened crust, subducting lithosphere and surrounding asthenosphere produces strong and pervasive anisotropy in the upper mantle. Shear wave splitting measurements, the most adopted method to image seismic anisotropy so far, when interpreted in a ray-based framework result in little or no depth resolution, hampering a correct image of the anisotropy distribution with depth. In this study, we aim to better constrain the depth-dependent seismic anisotropy beneath Italy and surrounding regions, by isolating for the first time the source region of anisotropy at different depths. To do that, we perform an anisotropy tomography, adopting the splitting intensity inversion method. It is entirely based on the finite-frequency effect in the splitting of SKS waves. We first computed the splitting intensity using SKS waves recorded at all available permanent and temporary stations over the region, obtaining a huge dataset of measurements used as an input for the tomographic inversion. The large-scale 3D model of seismic anisotropy obtained with the inversion shows a clear change of anisotropy properties in terms of fast polarisation direction and intensity for different depths, thus improving the characterization of the main sources of anisotropy in the mantle as a function of depth. Shallower layers (70–100 km depth) are characterised by a complex and variable oriented pattern of anisotropy fast direction and intensity, which becomes progressively more organised with depth (100–300 km). This pattern suggests a strong control exerted by the geometry and motion of the different slab segments and the large-scale asthenospheric flow generated by subduction and roll-back processes. The strength of anisotropy increases with depth, with high values affecting the bulge of the Alps and Apennines chains and the southern Tyrrhenian subduction system. On the contrary, weaker anisotropy characterises the transition zone from the Apennines to Alpine domains beneath the Po plain, and both the Adriatic and European domains.

Heat and mass transfer visualisation of an exothermic acid-base microfluidic reactor using infrared thermospectroscopy

ABSTRACT Here, a microfluidic reactor that is transparent in the mid-wave infrared spectrum with an effective path length of 38 µm is developed for characterisation via operando Fourier-transform Infrared (FTIR) thermospectroscopy. This imaging technique couples an infrared (IR) camera with an FTIR spectrometer to quantify heat and mass transfer in the exothermic acid-base reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH). The absorbance fields of the reaction are used to simultaneously derive the molar concentration fields of the reactants (HCl and NaOH) and products (sodium chloride [NaCl]) at the microscale through a linear inverse method. The heat generated at the reaction interface is visualised through a thermal field captured from the measured proper emission. Concentration and thermal fields are then compared to an advection-diffusion model for validation. The results proposed in this work present a refined contactless calorimetry process for characterising the heat and mass transport in an acid-base reaction. Further refinement of this work will enable accurate and non-invasive measurements for the enthalpy of reaction in chemical reactions.

Integration of geographic features and bathymetric inversion in the Yangtze River's Nantong Channel using gradient boosting machine algorithm with ZY-1E satellite and multibeam data

This study investigates the integration of geographic features from ZY-1E satellite data with advanced machine learning techniques to enhance water depth inversion in the Yangtze River's Nantong Channel. Utilizing the Gradient Boosting Machine (GBM) and its geospatially enhanced version, GBM-Lon./Lat., significant improvements in modeling precision were observed, as reflected by lower RMSE and higher R² values compared to traditional depth inversion methods. The research underscores the benefits of incorporating geospatial data, which allows for a more nuanced understanding of the hydrological dynamics and facilitates more accurate predictions in the turbid waters of the channel. Challenges such as atmospheric effects, water turbidity, and data acquisition issues under variable weather conditions were identified. The study proposes further optimization of these models to handle diverse environmental conditions and enhance the accuracy of bathymetric mapping. The integration of machine learning with remote sensing not only supports navigational safety and efficient waterway management but also contributes significantly to environmental monitoring and sustainable riverine infrastructure development.

Phase fraction measurement of gas-liquid flow based on cyclonic capacitive sensor (CCS) and inverse drift flux method

Abstract As the demand for clean energy sources like natural gas increases, the need for methods to measure the phase fraction of gas-liquid two-phase flows, which have complex and variable flow patterns, becomes more pronounced. This study introduces a phase fraction measurement method based on a cyclonic capacitive sensor. An effective phase fraction prediction model for the gas-liquid flow measurement section is established based on the capacitive signals. Using the drift flux principle, the dimensionless drift velocity of the spiral annular flow is analyzed, and a volume gas fraction (GVF) prediction model based on the ‘inverse drift flux method’ is established. Experimental results show that this method is suitable for a wide range of phase fraction measurements and is highly accurate. When the liquid volume fraction (LVF) is less than 10%, the average relative error of the predicted GVF is 0.3%; for the LVF from 10% to 30%, the average relative error is 1.4%.

Zastosowanie Metody Elementów Skończonych do analizy metody określania rozmiaru buta na podstawie pomiarów pola magnetycznego

Paper presents utilization of Finite Element Method (FEM) for analysis of usefulness of shoe size assessment method, based on magnetovision measurements. Measurement method based on disturbances of the uniform magnetic field (e.g. Earth’s magnetic field) is presented. Disturbances are caused by loose material of high magnetic permeability placed inside the tested shoe, which adapts to the insides of the shoe. The disturbed magnetic field is measured by the matrix of magnetometers. The values of magnetic field are an input into inverse transformation algorithm which fits the position of matrix sensors into the reference (obtained by FEM) distribution of magnetic field. Based on the fitted parameters of sensors matrix a ratio between the measured and reference shoe size was determined. A FEM-based forward transformation is presented, which allows for generation of three-dimensional array of magnetic field distribution. Initial tests of inverse transformation were conducted successfully. Next steps consisted of tests of inverse transformation method with an inclusion of the typical measurement noise. A FEM-based forward transformation was conducted of a modified shoe model (including simplified screw model). Inverse transformation was conducted but both influence of measurement noise, as well as the presence of additional high permeability material, resulted that the presented shoe size assessment method is not suitable for practical implementation.

Performance assessment of sentinel-3/6 altimeter data for marine gravity recovery

High-precision sea surface height is crucial for determining the marine gravity field. The Sentinel-3/6 altimetry missions, equipped with SRAL and Poseidon-4 altimeters, provide this essential data. However, there is a lack of comprehensive assessment of the Sentinel-3/6 altimeters for inverting marine gravity anomalies (MGA). In this study, we employ the inverse Venning-Meinsz method to derive nine sets of 1’×1’ MGAs in the South China Sea (SCS) and the Ross Sea (RS). Specifically, MGAs from Sentinel-3A, Sentinel-3B, Sentinel-6 SARM, Sentinel-6 LRM, HY-2A, ICESat-2, and CryoSat-2 are denoted as S3A, S3B, S6S, S6L, H2A, IS2, and CS2, respectively. MGA from the combined HY-2A, ICESat-2, and CryoSat-2 is referred to as HIC, while 3SHIC denotes the MGA from the combination of Sentinel-3/6 SARM, HY2A, ICESat-2, and CryoSat-2. We assess the performance of these MGAs using the EGM08, DTU17, SIO V32.1, and SDUST2021 gravity field models, as well as shipboard gravity across different ocean regions. Among the Sentinel-3/6 MGAs, S3B exhibits the highest accuracy in the SCS, with a root mean square error (RMSE) of 5.277 mGal, followed closely by S3A. Conversely, S3A demonstrates the highest accuracy with an RMSE of 4.635 mGal, followed by S3B in the RS. The inversion accuracy of MGAs from S6S and S6L are comparable, though S6S outperforms S6L in the open sea. The performance of MGAs from Sentinel-3/6 matches or surpasses that of other altimetry missions during the same period. In the SCS, the best-performing MGA is 3SHIC, with an RMSE of 4.585 mGal, closely matching DTU17. However, 3SHIC exhibits superior performance in the RS with an RMSE of 4.263 mGal compared to DTU17 and SDUST 2021. Furthermore, the performance of 3SHIC, which integrates Sentinel-3/6 data, improves that of HIC by 0.74% and 3.37% in the SCS and RS, respectively. These results underscore the contribution of Sentinel-3/6 altimeters to the MGA, particularly in coastal and high-latitude regions. Integration of Sentinel-3/6 data with other altimetry satellites is expected to enhance the spatial resolution and accuracy of the global marine gravity field, especially with the successful establishment of the network of Sentinel-6 in the future.

Formation Control with Feedback Nash Strategy for Multiple Unmanned Aerial Vehicles in Unknown Environments

In the paper, the formation control problem in unknown environments for networked multi-unmanned aerial vehicle systems (UAVSs) is resolved under a nonlinear differential game (NL-DDG) framework. The main challenge of this framework is how to obtain feedback Nash strategies, which typically overly rely on global information and cannot ensure the existence of Nash strategies in unknown environments. Toward this goal, we initially design collision avoidance rules to ensure the safety of each UAV. Subsequently, we utilize an inverse optimal control method to construct the NL-DDG that incorporates both formation control and collision avoidance costs, enabling the derivation of analytical forms of Nash strategies relying solely on local information and minimizing performance metrics. In addition, the existence of feedback Nash strategy can be guaranteed with an undirected and connected information topology, which represents the optimality for the UAVSs. Moreover, we analyze the stability of the closed-loop system. Finally, the simulation results validate the effectiveness of the proposed scheme.

Impact of titanium dioxide/graphene in polyvinylidene fluoride nanocomposite membrane to intensify methylene blue dye removal, antifouling performance, and reusability

AbstractThe development of efficient water purification technologies is a critical research focus driven by the crucial role of clean water sources for ecological sustainability. This study explores the strategic incorporation of nanoparticles within polyvinylidene fluoride (PVDF) membranes as a promising approach to enhance membrane performance for wastewater remediation. PVDF membranes containing varying ratios of graphene (GR) and titanium dioxide (TiO2) nanocomposites were fabricated via phase inversion method. Characterization techniques including XRD, FTIR, and FESEM‐EDX revealed that the 80% GR nanocomposite membrane exhibited desirable structural and functional properties with pronounced sponge‐like morphology and homogenous nanoparticle distribution. Fourier‐transform infrared spectroscopy and x‐ray diffraction analysis confirmed the 80% GR membrane retained PVDF crystallinity while uniquely eliminating TiO2 crystallinity. Subsequently, performance testing demonstrated the 80% GR nanocomposite membrane had the highest water flux and methylene blue dye rejection rates compared to other ratios and the pristine PVDF membrane. Both fabricated membranes exhibited sufficient reusability and antifouling properties. However, 80% GR ratio exhibited superior antifouling properties, indicating its potential as an optimal material for improving membrane hydrophilicity and overall water purification technologies. These findings underscore the strategic utility of GR‐TiO2 nanocomposites for enhancing PVDF membrane performance in sustainable wastewater treatment applications.

Semi-analytic three-shell forward calculation for magnetoencephalography

In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.

A Method by using predefined windows to improve the InSAR atmospheric correction model based on GNSS ZTD and its horizontal delay gradient

ABSTRACT Correcting the signal delay caused by electromagnetic waves passing through the atmosphere is crucial in InSAR. Atmospheric delays are significant enough to obscure the true deformation signal, making it difficult for InSAR to detect deformation signals at the millimetre scale. Therefore, it is imperative to mitigate atmospheric interference appropriately. To interpolate sparse GNSS networks and capture small-scale atmospheric delays, this study presents an enhanced method for constructing an atmospheric correction model based on GNSS Zenith Total Delay (ZTD) and its horizontal gradient, which is integrated within a predefined window. To validate the effectiveness of the improved model, we applied it to 27 InSAR short-time and short-spatial baseline unwrapped interferograms. These interferograms are composed of images observed by the Sentinel-1A satellite from January to December 2022 in Southern California. The corrective impact of the enhanced model is also compared against that of the initial inversion model and GACOS to confirm the viability of the approach. Results of the evaluation, considering root mean square error (RMSE), standard deviation (STD), and the correlation between phase and elevation, indicate that our enhanced method reduces correction errors by 35.10%, 20.05%, and 63.52%, respectively, compared to GACOS. Compared to the initial model, these reductions are 58.19%, 57.23%, and 4.34%, respectively. By integrating the outcomes from all three evaluation methods and analysing the corrected images, our enhanced model effectively resolves the inconsistency in correction effects resulting from the spatial variability of atmospheric delay. Moreover, incorporating the horizontal gradient in the inversion method has proven effective in capturing small-scale atmospheric delay signals. This highlights the feasibility and benefits of our enhanced model.

Comparison of optimized effective potential with inverse Kohn-Sham method for Hartree-Fock exchange energy.

The inverse Kohn-Sham (inv-KS) density-functional theory for the electron density of the Hartree-Fock (HF) wave function was revisited within the context of the optimized effective potential (HF-OEP). First, we clarify the relationship between the inv-KS and the HF-OEP within the framework of the potential-functional theory. The similarities and the differences of the approaches are then discussed on the basis of their methodological details, which motivates comparisons of the wave function provided by each method. Next, the real-space grid implementations of the inv-KS and the HF-OEP are addressed for the comparisons. The total HF energies EHF[{φiinv-KS}] for the wave functions φiinv-KS on the effective potentials optimized by the inv-KS are computed for a set of small molecules. It is found that the mean absolute deviation (MAD) of EHF[{φiinv-KS}] from the HF energy is clearly smaller than the MAD of EHF[{φiOEP}], demonstrating that the inv-KS is advantageous in constructing the detailed structure of the exchange potential υx as compared with the HF-OEP. The inv-KS method is also applied to an ortho-benzyne radical known as a strongly correlated polyatomic molecule. It is revealed that the spin populations on the atomic sites computed by the UHF calculation can be faithfully reproduced by the wave functions on the inv-KS potential.