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This study aims to investigate the possible use of a deep neural network (DNN) as an inverse solver.

Different models based on DNNs are designed and proposed for the resolution of inverse electromagnetic problems either as fast solvers for the direct problem or as straightforward inverse problem solvers, with reference to the TEAM 25 benchmark problem for the sake of exemplification.

Using DNNs as straightforward inverse problem solvers has relevant advantages in terms of promptness but requires a careful treatment of the underlying problem ill-posedness.

This work is one of the first attempts to exploit DNNs for inverse problem resolution in low-frequency electromagnetism. Results on the TEAM 25 test problem show the potential effectiveness of the approach but also highlight the need for a careful choice of the training data set.

The purpose of this study is to estimate inputs (outputs) and flexible measures when outputs (inputs) are changed provided that the relative efficiency values remain without change.

A novel inverse data envelopment analysis (DEA) approach with flexible measures is proposed in this research to assess inputs (outputs) and flexible measures when outputs (inputs) are perturbed on condition that the relative efficiency scores remain unchanged. Furthermore, flexible inverse DEA approaches proposed in this study are used for a numerical example from the literature and an application of Iranian banking industry to clarify and validate them.

The findings show that including flexible measures into the investigation effects on the changes of performance measures estimated and leads to more reasonable achievements.

The traditional inverse DEA models usually investigate the changes of some determinate input-output factors for the changes of other given input-output indicators assuming that the efficiency values are preserved. However, there are situations that the changes of performance measures should be tackled while some measures, called flexible measures, can play either input or output roles. Accordingly, inverse DEA optimization models with flexible measures are rendered in this paper to address these issues.

The purpose of this paper is to present a simple approach for calculation of the sensitivities in the free-form inverse design problems. The approach is based on the analogy with the similar tasks used in the signal-processing analysis. In the proposed case it is not required to solve an adjoint problem as in the most of the similar optimization tasks. The simulation engine used in the background is a Fast Boundary Element Method. The approach is validated on some known benchmark problems.

Inverse design is recognized nowadays as a crucial scientific grand challenge. Contrary to the conventional approach (“Given the structure, find the properties”) it purses a new paradigm (“Given the desired property, find the structure”). Inverse class of problems has a broad application area, from the material-, medical-, bio- to the engineering-class of problems. When dealing with the inverse design in free-form optimization of the engineering problems the typical approach is to calculate the adjoint problem. Calculation of the adjoint problem mostly requires the costly calculation of the gradients, which makes the whole optimization procedure rather expensive due to the high computational burden required for their solution.

In this paper it is proposed a novel Simple Sensitivity Approach to get in a fast way the response (sensitivity) function of the analyzed structure. The simulation engine used in the background is the Fast Boundary Element Method.

Novel approach for inverse design when performing the free-form optimization of engineering problems.

The purpose of this paper is to develop an inverse approach for 3D thermal sources determination.

The developed approach is based on the Green's function for Poison's equation. Forward and inverse couple electromagnetic‐thermal field problems are formulated. Finite elements models are built and applied. Thermal field data are acquired by thermo vision camera. The thermal field sources are determined inside of the investigated inaccessible volume object using modeled and measured data with the developed approach.

The presented method and implemented examples demonstrate the possibilities of the developed approach for inverse source problem solution and determination of thermal field distributions of electrical devices.

The proposed inverse method uses the Green's function for Poison's equation for solution of thermal field problem taking into account the couple electromagnetic‐thermal problems. Proposed inverse method is very fast, accurate and can be used in many practical activities for electrical current determination and visualization in inaccessible regions only by measured external thermal field. Thermal field data needed for the method are easily acquired by thermo vision camera.

Inverse problems deal with determining the causes on the basis of knowing their effects. The object of the inverse parameter estimation problem is to fix the thermal material parameters (the cause) on the strength of a given observation of the temperature history at one or more interior points (the effect). This paper demonstrates two novel approaches to the inverse problems. These approaches use two artificial intelligence mechanisms: neural network and genetic algorithm. Examples shown in this paper give a comparison of results obtained by both of these methods. The numerical technique of neural networks evolved from the effort to model the function of the human brain and the genetic algorithms model the evolutional process of nature. Both of the presented approaches can lead to a solution without having problems with the stability of the inverse task. Both methods are suitable for parallel processing and are advantageous for a multiprocessor computer architecture.

This paper presents a review concerning the analytical and inverse methods of small punch creep test (SPCT) in order to evaluate the mechanical property of component material at elevated temperature.

In this work, the effects of temperature, specimen size and shape on material properties are mainly discussed using the finite element (FE) method. The analytical approaches including membrane stretching, empirical or semi-empirical solutions that are currently used for data interpretation have been presented.

The state-of-the-art research progress on the inverse method, such as non-linear optimization program and neutral network, is critically reviewed. The capabilities of the inverse technique, the uniqueness of the solution and future development are discussed.

The state-of-the-art research progress on the inverse method such as non-linear optimization program and neutral network is critically reviewed. The capabilities of the inverse technique, the uniqueness of the solution and future development are discussed.

In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

Nowadays, simplified inverse or one step approaches for the sheet forming modeling are increasingly used in the automobile industry, since they allow to quickly realize the preliminary design and especially to optimize the process parameters. These methods often based on implicit static algorithms cause sometimes convergence problems because of strong non‐linearities. This paper deals with several initial guess methods to speed up the convergence of the implicit static solver used in the inverse approach for stamping modeling. The blank's mesh as initial solution is obtained by geometrical considerations based on the known shape of the final 3D workpiece. Three algorithms for the estimation of the blank's mesh have been developed and compared. The application to several industrial problems shows their efficiency and performance.

Focuses on the inverse problems arising from the simulation of forming processes. Considers two sets of problems: parameter identification and shape optimization. Both are solved using an optimization method for the minimization of a suitable objective function. The convergence and convergence rate of the method depend on the accuracy of the derivatives of this function. The sensitivity analysis is based on a discrete approach, e.g. the differentiation of the discrete problem equations. Describes the method for non‐linear, non‐steady‐state‐forming problems involving contact evolution. First, it is applied to the parameter identification and to the torsion test. It shows good convergence properties and proves to be very efficient for the identification of the material behaviour. Then, it is applied to the tool shape optimization in forging for a two‐step process. A few iterations of the inverse method make it possible to suggest a suitable shape for the preforming tools.

Prompted by the reliability and robustness of the previously proposed method of non-destructive measurement of thermal conductivity (TC) for anisotropic materials, the enhanced approach is presented in this study. The main improvement lies in the substitution of the analytic solution of direct problem solver with a numerical one. This solver, used during the inverse procedure that fits measurement data into simulated ones, is proposed to be a numerical one (finite volume method). Moreover, the purpose of this study is to show the applicability of the reduce order model for retrieving thermal conductivity of solid body.

In the proposed methodology, both the laser heat source and temperature measurements are performed on the same side of the sample material, which is the main difference with respect to the classic Parker flash method. To speed up the computational time, the full numerical model used in the course of inverse solution is replaced by the proper orthogonal decomposition (POD)-radial basis function (RBF) reduced order model, which is fast and accurate.

The TCs measured using the proposed methodology are in good agreement with the well established (but destructive) measurement methods. The advantage of the proposed approach lies in the optimal approximation properties of the POD approximation basis used in reduced order model, as well as in its regularization properties.

The proposed technique has high application potential in the design of novel apparatus for non-destructive measurement of TCs for both isotropic and anisotropic materials.

This is the first time when the POD-RBF reduced order model is used in the procedure of non-destructive TC measurement for anisotropic bodies.