Inversion Algorithm Research Articles

Implementing new computational methods for the study of JCT and SC inner wall basement membrane biomechanics and hydrodynamics

PurposeThe conventional aqueous outflow pathway, which includes the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and the inner wall endothelium of Schlemm's canal (SC), regulates intraocular pressure (IOP) by controlling the aqueous humor outflow resistance. Despite its importance, our understanding of the biomechanics and hydrodynamics within this region remains limited. Fluid-structure interaction (FSI) offers a way to estimate the biomechanical properties of the JCT and SC under various loading and boundary conditions, providing valuable insights that are beyond the reach of current imaging techniques. MethodsIn this study, a normal human eye was fixed at a pressure of 7 mm Hg, and two radial wedges of the TM tissues, which included the SC inner wall basement membrane and JCT, were dissected, processed, and imaged using 3D serial block-face scanning electron microscopy (SBF-SEM). Four different sets of images were used to create 3D finite element (FE) models of the JCT and inner wall endothelial cells of SC with their basement membrane. The outer JCT portion was carefully removed as the outflow resistance is not in that region, leaving only the SCE inner wall and a few µm of the tissue, which does contain the resistance. An inverse iterative FE algorithm was then utilized to calculate the unloaded geometry of the JCT/SC complex at an aqueous humor pressure of 0 mm Hg. Then in the model, the intertrabecular spaces, pores, and giant vacuole contents were replaced by aqueous humor, and FSI was employed to pressurize the JCT/SC complex from 0 to 15 mm Hg. ResultsIn the JCT/SC complex, the shear stress of the aqueous humor is not evenly distributed. Areas proximal to the inner wall of SC experience larger stresses, reaching up to 10 Pa, while those closer to the JCT undergo lower stresses, approximately 4 Pa. Within this complex, giant vacuoles with or without I-pore behave differently. Those without I-pores experience a more significant strain, around 14%, compared to those with I-pores, where the strain is roughly 9%. ConclusionsThe distribution of aqueous humor wall shear stress is not uniform within the JCT/SC complex, which may contribute to our understanding of the underlying selective mechanisms in the pathway.

Application of Inverse Design Approaches to the Discovery of Nonlinear Optical Switches.

Molecular switches, in which a stimulus induces a large and reversible change in molecular properties, are of significant interest in the domain of photonics. Due to their commutable redox states with distinct nonlinear optical (NLO) properties, hexaphyrins have emerged as a novel platform for multistate switches in nanoelectronics. In this study, we employ an inverse design algorithm to find functionalized 26R→28R redox switches with maximal βHRS contrast. We focus on the role of core modifications, since a synergistic effect with meso-substitutions was recently found for the 30R-based switch. In contrast to these findings, the inverse design optima and subsequent database analysis of 26R-based switches confirm that core modifications are generally not favored when high NLO contrasts are targeted. Moreover, while push-pull combinations enhance the NLO contrast for both redox switches, they prefer a different arrangement in terms of electron-donating and electron-withdrawing functional groups. Finally, we aim at designing a three-state 26R→28R→ 30R switch with a similar NLO response for both ON states. Even though our best-performing three-state switch follows the design rules of the 30R-based component, our chemical compound space plots show that well-performing three-state switches can be found in regions shared by high-responsive 26R and 30R structures.

Adaptive Spectral Inversion for inverse medium problems

A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based representations, the misfit is instead minimized in a small subspace spanned by the first few eigenfunctions of a judicious elliptic operator, which itself depends on the previous iteration. By repeatedly adapting both the dimension and the basis of the search space, regularization is inherently incorporated at each iteration without the need for extra Tikhonov penalization. Convergence is proved under an angle condition, which is included into the resulting Adaptive Spectral Inversion (ASI) algorithm. The ASI approach compares favorably to standard grid-based inversion using L 2-Tikhonov regularization when applied to an elliptic inverse problem. The improved accuracy resulting from the newly included angle condition is further demonstrated via numerical experiments from time-dependent inverse scattering problems.

Spacecraft Segment Damage Identification Method Based on Fiber Optic Strain Difference Field Reconstruction and Norm Calculation

Real-time online identification of spacecraft segment damage is of great significance for realizing spacecraft structural health monitoring and life prediction. In this paper, a damage response characteristic field inversion algorithm based on the differential reconstruction of strain response is proposed to solve the problem of not being able to recognize the small damages of spacecraft structure directly by the strain response alone. Four crack damage location identification methods based on vector norm computation are proposed, which realize online identification and precise location of structural damage events without external excitation by means of spacecraft structural working loads only. A spacecraft segment structural damage monitoring system based on fiber optic grating sensors was constructed, and the average error of damage localization based on the curvature vector 2 norm calculation was 2.58 mm, and the root-mean-square error was 1.98 mm. The results show that the method has superior engineering applicability for on-orbit service environments.

Adaptive Satellite Navigation Anti-Interference Algorithm Based on Inverse Cosine Function

Contrasting the dilemma that the traditional time-domain least mean square (LMS) algorithm in the existing satellite navigation receiver anti-interference system cannot satisfy the convergence time is short and maintain a low level of steady-state error at the same time, an inverse cosine variable step size LMS algorithm (ICVS-LMS) is proposed. To begin with, the LMS algorithm, with a fixed step size focuses on its effectiveness in attenuating and suppressing interference signals, is analyzed, and then the proposed ICVS-LMS algorithm is analyzed. In conclusion, both the ICVS-LMS algorithm and the traditional algorithm are simulated and compared in terms of their effectiveness in suppressing interference in satellite navigation signals. The experimental results demonstrate that the improved algorithm significantly reduces convergence time while maintaining a small steady-state error. The improved algorithm demonstrates high robustness and an obvious suppression effect on interference signals. The anti-interference performance is 8.41–12.22% higher than that of the proposed algorithm.

Modeling and simulation of successive breakdown events in thin gate dielectrics using standard reliability growth models

The application of constant electrical stress to a metal–insulator-semiconductor (MOS) or metal–insulator-metal (MIM) structure can generate multiple breakdown events in the dielectric film. Very often, these events are detected as small jumps in the current–time characteristic of the device under test and can be treated from the stochastic viewpoint as a counting process. In this letter, a wide variety of standard reliability growth models for this process are assessed in order to determine which option provides the best simulation results compatible with the experimental observations. For the generation of the breakdown event arrivals, two alternative stochastic methods for the power-law Poisson process are investigated: first, the inversion algorithm for the cumulative distribution function and second, an on-the-fly method based on the so-called rejection algorithm. Though both methods are equivalent, the first one is more appropriate for data analysis using spreadsheet calculations while the second one is highly suitable for circuit simulation environments like LTSpice. The connection of the selected nonhomogeneous Poisson process with the Weibull model for dielectric breakdown is also discussed.

Magnetic inversion approach for modeling data acquired across faults: various environmental cases studies

An effective extension to the particle swarm optimizer scheme has been developed to visualize and modelize robustly magnetic data acquired across vertical or dipping faults. This method can be applied to magnetic data sets that support various investigations, including mining, fault hazards assessment, and hydrocarbon exploration. The inversion algorithm is established depending on the second horizontal derivative technique and the particle swarm optimizer algorithm and was utilized for multi-source models. Herein, the inversion method is applied to three synthetic models (a dipping fault model contaminated without and with different Gaussian noises levels, a dipping fault model affected by regional anomaly, and a multi-source model) and three real datasets from India, Australia, and Egypt, respectively. The output models confirm the inversion approach’s accuracy, applicability, and efficacy. Also, the results obtained from the suggested approach have been correlated with those from other methods published in the literature.

Generalized inverse matrix-graphic deep learning algorithm for multispectral pyrometer temperature inversion.

The multispectral radiometric temperature measurement technique is affected by the unknown emissivity, and there is no multispectral radiometric temperature inversion algorithm applicable to any scene or target. To address the above problems, this paper converts the multispectral radiometric temperature inversion problem into an image recognition problem containing the temperature information to be measured, and proposes a graphical multispectral radiometric temperature adaptive inversion algorithm. In this paper, we use the difference between spectral channels to convert the one-dimensional radiation data into a two-dimensional radiation map; use the generalized inverse to obtain the spectral emissivity distribution features, fuse them with the two-dimensional radiation map, and use an improved deep learning network to achieve adaptive temperature inversion. It is experimentally verified that the algorithm proposed in this paper can achieve simultaneous inversion of temperature and emissivity for any scene or target with sufficient data set.

Inverse design of an ultra-compact and large-bandwidth bent subwavelength grating wavelength demultiplexer.

Inverse design has attracted significant attention as a method to improve device performance and compactness. In this research, we employed a combination of forward design and the inverse algorithm using particle swarm optimization (PSO) to design a bent ultra-compact 1310/1550nm broadband wavelength demultiplexer assisted by a subwavelength grating (SWG). Through the phase matching at 1550nm and the phase mismatch at 1310nm, we rapidly designed the width parameters of SWG in the forward direction. Then the PSO algorithm was used to optimize the SWG parameters in a certain range to achieve the best performance. Additionally, we introduced a new bent dimension significantly reducing the device length while maintaining low insertion loss (IL) and high extinction ratios (ERs). It has been verified that the length of the device is only 7.8µm, and it provides a high ER of 24dB at 1310nm and 27dB at 1550nm. The transmitted spectrum shows that the IL values at both wavelengths are below 0.1dB. Meanwhile, the 1dB bandwidth exceeds 150nm, effectively covering the entire O-band and C-band. This approach has been proven successful in enhancing performance and significantly reducing the device footprint.

A review of regularization strategies and solution techniques for ill-posed inverse problems, with application to inverse heat transfer problems

With the presence of a large number of inversion algorithms for inverse heat transfer problems (IHTPs) and non-IHTPs, a need for review to have a holistic view is seen. An exhaustive literature review, with the motivation of selecting the inversion technique best fit for a given problem, was made for a general inverse problem. For ill-posedness, a classification of available regularization algorithms namely Tikhonov’s regularization, Bayesian regularization, mollification method, Beck’s sequential approach and Alifanov’s iterative approach, has been provided. Inversion methods like singular value decomposition, truncated singular value decomposition, Tikhonov regularization and total variation regularization are explained. Optimization methods namely steepest descent method, conjugate gradient method, Newton method, Levenberg–Marquardt method, Lagrange method, adjoint method, function specification method, genetic algorithm, differential evolution and particle swarm optimization (PSO) are reviewed. Further, a technique based on neural networks is studied, and wavelet methods like shrinking and wavelet vaguelette decomposition are reviewed. Associated literature has also been listed, highlighting the gaps. The usability of various algorithms in IHTP, starting from the golden section search method, for retrieval of a single parameter, to the regularized versions of the inversion technique, for retrieval of multiple parameters with uncertainty, demonstrates real-life applications to fins in IHTP. An inversion algorithm capable to handle every kind of nonlinearity is sought in literature, whose absence raises the research question, “Is there a technique that works globally for every inverse problem?”, is asked prior to, “What if the available techniques were not utilized to an extent that they should?” is posed. In lieu of this gap, a general comparative framework is developed, such that an efficient technique is selected, based on the total minimum error, which can be used in any field of interest.

A Time-Optimal Continuous Jerk Trajectory Planning Algorithm for Manipulators

In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time.

Implementation of dynamics inversion algorithms in active vibration control systems: Practical guidelines

It is common that excessive vibrations problems arise in modern slender, low-damping, lightweight structures such as footbridges or long-span floors subjected to human actions. The integration of inertial vibration controllers has been extensively used to mitigate the problems associated with vibration serviceability of such structures. Among them, the active vibration absorber constitutes the most sophisticated and effective alternative. Nonetheless, the inherent dynamics of the actuators used in the practical implementations of these systems may negatively affect their performance, compromising the overall system stability and performance. In this work, the practical application of dynamics inversion techniques to the force control of electrodynamic proof-mass actuators employed as active vibration absorption systems in lightweight structures subjected to human-induced vibrations is presented. The main idea behind the dynamics inversion approach is to find an approximate inverse of the actuator system which, upon implementation on a real-time controller, approximately cancels out actuator dynamics leading to an improved force tracking, with the subsequent enhancement in the performance of any force-based vibration control algorithm. The dynamics inversion has been applied to the classical direct velocity feedback approach, leading to a novel vibration control algorithm denominated velocity feedback with dynamics inversion. Additionally, the stability of the suggested method has been studied and practical guidelines, including a step-by-step design procedure, have been provided for researchers willing to apply the proposed algorithm. The goodness of the suggested method has been assessed by means of a tests campaign carried over an existing glass fiber reinforced polymer footbridge, which fulfills the static requirements at Serviceability and Ultimate Limit States, but exhibits excessive vibrations when its first resonance frequency is excited. Two types of tests have been performed: a walking load and a vandal bouncing excitation exerted at the midspan of the footbridge. In both cases, the experimental results show that the new procedure outperforms the classical velocity feedback approach thanks to the enhanced force tracking, leading to a remarkable reduction in the vibrations experimented by the structure under study.

Feature-based magnetotelluric inversion by variational autoencoder using a subdomain encoding scheme

Magnetotelluric (MT) data inversion aims to reconstruct a subsurface resistivity model that minimizes the discrepancy between inverted and measured electromagnetic data. Conventional pixel-based minimum-structure inversion often yields a smoothed-out reconstruction with a relatively low resolution. A priori geophysical knowledge can be embedded into inversion and improve the reconstruction resolution through proper reparameterization. However, existing reparameterization approaches, such as model-based and parametric transform-based inversion, have limited ability to incorporate various a priori information. The effectiveness of existing deep generative model-based inversion algorithms is still debatable when applied to scenarios with complex backgrounds. We develop a feature-based MT data inversion method based on a variational autoencoder (VAE) with a subdomain encoding scheme. Instead of encoding the entire domain of an investigation, we adopt a 1D subdomain encoding scheme to encode the 1D resistivity-depth models using a single VAE. The latent variables for the 2D model are a combination of the latent variables for 1D models, and the encoded region of interest (ROI) can be flexibly determined. The latent variables of ROI and the pixels outside the ROI are simultaneously inverted using the gradient-descent method. Our 1D subdomain encoding scheme reduces the complexity and diversity of the data set, and it can flexibly embed a priori knowledge with various uncertainties. Synthetic data inversion and inversion of the Southern African Magnetotelluric Experiment field data validate our method’s ability to effectively improve inversion accuracy and resolution.

An Enhanced Atmospheric Pre-Corrected Differential Absorption (APDA) Algorithm by Extending LUTs Applied to Analyze ZY1-02D Hyperspectral Images

Water vapor is a crucial component of the atmosphere. Its absorption significantly influences remote sensing by impacting radiation signals transmitted through the atmosphere. Determining columnar water vapor (CWV) from hyperspectral remote sensing data is essential during the imagery atmospheric correction process. Over the past 40 years, numerous CWV inversion algorithms have been developed, with refinements to enhance retrieval accuracy and reliability. In this study, we proposed an enhanced atmospheric pre-corrected differential absorption (APDA) algorithm. This enhancement was achieved by thoroughly analyzing water vapor absorption in relation to elevation and aerosol optical depth and extending look up tables (LUTs). The enhanced method utilizes a pre-built MODTRAN lookup table and is applied to ZY1-02D hyperspectral data from a satellite launched in 2020. We compared the inversion results of 10 ZY1-02D scenes obtained using the improved method with AERONET measurements and inversion results from commonly used atmospheric correction software, namely, FLAASH and ATCOR. The updated algorithm demonstrated a lower average error (0.0568 g·cm−2) and relative average error (10.49%) compared to the ATCOR software (0.17 g·cm−2 and 40.78%, respectively) and the FLAASH module (0.13 g·cm−2 and 30.82%, respectively). Consequently, the enhanced method outperforms traditional CWV inversion algorithms, especially at high altitudes.

Three-Dimensional Limited-Memory BFGS Inversion of Magnetic Data Based on a Multiplicative Objective Function

At present, the traditional magnetic three-dimensional inversion method has been fully developed and is widely used. Magnetic exploration is a kind of geophysical exploration method that uses the magnetic field changes (magnetic anomalies) caused by the magnetic differences between various rocks in the crust to find useful mineral resources and study the underground structure. Traditional magnetic three-dimensional inversion is relatively inefficient. Moreover, the traditional additive objective function (data fitting difference term plus regularization term and logarithmic obstacle term), which causes the regularization factor selection to be more complicated, is implemented in this method. Therefore, it is necessary to establish a new efficient three-dimensional magnetic inversion algorithm and optimize the selection of regularization factors. In this paper, based on the limited-memory BFGS (L-BFGS) method, the three-dimensional magnetic inversion of a multiplicative objective function is realized. The inversion test is conducted in this paper using both theoretical synthesis data and measured data. The results demonstrate that the limited-memory BFGS method significantly enhances the inversion efficiency and yields superior inversion outcomes compared to traditional magnetic three-dimensional inversion methods. Additionally, the multiplicative objective function-based three-dimensional magnetic inversion method simplifies the process of selecting weight factors for regularization terms.

A Method for Estimating Alfalfa (Medicago sativa L.) Forage Yield Based on Remote Sensing Data

Alfalfa (Medicago sativa L.) is a widely planted perennial legume forage plant with excellent quality and high yield. In production, it is very important to determine alfalfa growth dynamics and forage yield in a timely and accurate manner. This study focused on inverse algorithms for predicting alfalfa forage yield in large-scale alfalfa production. We carried out forage yield and aboveground biomass (AGB) field surveys at different times in 2022. The correlations among the reflectance of different satellite remote sensing bands, vegetation indices, and alfalfa forage yield/AGB were analyzed, additionally the suitable bands and vegetation indices for alfalfa forage yield inversion algorithms were screened, and the performance of the statistical models and machine learning (ML) algorithms for alfalfa forage yield inversion were comparatively analyzed. The results showed that (1) regarding different harvest times, the alfalfa forage yield inversion model for first-harvest alfalfa had relatively large differences in growth, and the simulation accuracy of the alfalfa forage yield inversion model was higher than that for the other harvest times, with the growth of the second- and third-harvest alfalfa being more homogeneous and the simulation accuracy of the forage yield inversion model being relatively low. (2) In the alfalfa forage yield inversion model based on a single parameter, the moisture-related vegetation indices, such as the global vegetation moisture index (GVMI), normalized difference water index (NDWI) and normalized difference infrared index (NDII), had higher coefficients of correlation with alfalfa forage yield/AGB, and the coefficients of correlation R2 values for the first-harvest alfalfa were greater than 0.50, with the NDWI correlation being the best with an R2 value of 0.60. (3) For the alfalfa forage yield inversion model constructed with vegetation indices and band reflectance as multiparameter variables, the random forest (RF) and support vector machine (SVM) simulation accuracy was higher than that of the alfalfa forage yield inversion model based on a single parameter; the first-harvest alfalfa R2 values based on the multiparameter RF and SVM models were both 0.65, the root mean square errors (RMSEs) were 329.74 g/m2 and 332.32 g/m2, and the biases were −0.47 g/m2 and −2.24 g/m2, respectively. The vegetation indices related to plant water content can be considered using a single parameter inversion model for alfalfa forage yield, the vegetation indices and band reflectance can be considered using a multiparameter inversion model for alfalfa forage yield, and ML algorithms are also an optimal choice. The findings in this study can provide technical support for the effective and strategic production management of large-scale alfalfa.

Progress of Electrical Resistance Tomography Application in Oil and Gas Reservoirs for Development Dynamic Monitoring

Petroleum engineers need real-time understanding of the dynamic information of reservoirs and production in the development process, which is essential for the fine description of oil and gas reservoirs. Due to the non-invasive feature of electromagnetic waves, more and more oil and gas reservoirs have received attention to capture the development dynamics with electrical resistance tomography (ERT). By measuring the distribution of resistivity on the surface, the ERT can offer information on the subsurface media. The theory and foundation of the ERT technology are presented in this study in the context of monitoring oil and gas reservoir growth dynamics. The characteristics of ERT technology are analyzed, and the progress of ERT application in the development of monitoring dynamics in terms of residual oil distribution, detection of water-driven leading edge, and monitoring of fractures during hydraulic fracturing is reviewed, as well as the progress of ERT technology optimization, including forward and inverse algorithms. This review aims to promote further application of ERT in the field of reservoir dynamics monitoring because of its important engineering significance as well as its academic value in terms of improving production efficiency and reducing risk.

Shape reconstruction for an inverse biharmonic problem from partial Cauchy data

In this paper, we address the Robin inverse problem for the biharmonic equation in a simply connected domain, to reconstruct the geometric shape of a non‐accessible part of the boundary from a single measurement of Riquier–Neumann data on the accessible part of that boundary. Our approach extends the nonlinear boundary integral equation, to recover the shape of the boundary. We propose the Newton iterative technique based on the Fréchet derivatives to linearize the system and then establish an injectivity of the linearized system for certain Robin coefficients, as well as the iteration scheme to describe the inverse algorithm for recovering the shape with respect to the unknowns. The mathematical spirit of the proposed method will be presented, and to illustrate its feasibility, some numerical examples will be provided.

Ensemble Kalman Inversion for upstream parameter estimation and indirect streamflow correction: A simulation study

Data assimilation (DA) techniques such as the Ensemble Kalman filter (EnKF) and its extensions allow for real-time corrections of state-space models and model parameters based on an assumption of Gaussian error. The hydrological DA literature primarily documents applications of the EnKF to solve sequential state estimation problems. Recent advances in the DA literature demonstrate the potential of applying EnKF-based methods as efficient, derivative-free algorithms to solve various general Bayesian inverse problems, such as parameter estimation, while simultaneously providing Uncertainty Quantification (UQ). In this paper, the authors employ the Ensemble Kalman Inversion (EKI) algorithm to infer the distribution of a set of routing parameters. Through this correction, we improve streamflow at locations upstream of the gauged site in a virtual catchment setting. The algorithm enables learning spatially distributed routing parameters with observations available only at the outlet. The study reveals that this method sufficiently improves model performance throughout the basin. The performance of this method is demonstrated in a virtual catchment for three different model/data configurations. Favorable results, even with model misspecification, indicate that this method holds promise for operational application and more general hydrologic parameter estimation problems.

Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements

We consider the inverse problem to determine the number and locations of acoustic point sources from single low-frequency partial data. The problem is particularly challenging in the sense that the data is available only at a few locations which span a small aperture. Integrating the deep neural networks (DNNs) and Bayesian inversion, we propose a divide-and-conquer approach by dividing the inverse problem into three subproblems. The first subproblem is to determine the number of point sources, which is formulated as a common machine learning task—classification. A simple DNN is proposed and trained to predict the numbers of the point sources. The second subproblem is to reconstruct the (approximate) locations of the point sources. We formulate the problem as a nonlinear function with the input being the measured data and the output being a carefully elaborated location vector. Then a second DNN is proposed to learn the mapping and predict the location vector effectively. The location vector is post-processed to provide an indicator (image) function for the (approximate) locations of the point sources. The third subproblem is to improve the accuracy of the location prediction, for which we employ a Bayesian inversion algorithm. This divide-and-conquer approach can effectively treat both phase and phaseless data as demonstrated by various examples.