Статті в журналах: "Neural network inversion"

1

Sun, Yuhang, Yang Liu, Mi Zhang, and Haoran Zhang. "Inversion of low- to medium-frequency velocities and densities from AVO data using invertible neural networks." GEOPHYSICS 87, no. 3 (March 3, 2022): A37—A42. http://dx.doi.org/10.1190/geo2021-0450.1.

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Amplitude-variation-with-offset (AVO) inversion and neural networks (NN) are widely used to invert elastic parameters. With more constraints from well-log data, neural network-based inversion may estimate elastic parameters with greater precision and resolution than traditional AVO inversion; however, neural network approaches necessitate a massive number of reliable training samples. Furthermore, because the lack of low-frequency information in seismic gathers leads to multiple solutions of the inverse problem, both inversions rely heavily on proper low-frequency initial models. To mitigate the dependence of inversions on accurate training samples and initial models, we have adopted solving inverse problems with the recently developed invertible neural networks (INNs). Unlike conventional neural networks, which address the ambiguous inverse issues directly, INNs learn definite forward modeling and use additional latent variables to increase the uniqueness of solutions. Motivated by the newly developed neural networks, we adopt an INN-based AVO inversion method, which can reliably invert low- to medium-frequency velocities and densities with randomly generated easy-to-access data sets rather than trustworthy training samples or well-prepared initial models. Tests on synthetic and field data indicate that our method is feasible, antinoise capable, and practicable.

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2

FEI, DONGYU, JOHN T. KUO, and YU-CHIUNG TENG. "WAVEFORM INVERSION AND MULTI-LAYER NEURAL NETWORK." Journal of Computational Acoustics 03, no. 03 (September 1995): 175–202. http://dx.doi.org/10.1142/s0218396x95000082.

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This paper presents the concept of neural network inversion. The basic mathematical problem is to establish the mapping between two multi-dimensional spaces, addressing the continuous function mapping between two close intervals. It introduces the 3-layer neural network existence theorem and proves that the multi-layer neural network can approximate any continuous function in the sense of supernorm or mean-squares-norm, provided that the activation function is locally Riemann integrable and nonpolynomial. With an initial guess of the target parameter, which, in the present case, is acoustic velocity, in a prescribed sphere, which contains the true parameter, the neural network inversion method ensures the search reaching the global minima. The principle of the neural network inversion on the basis of the least-squares minimization (L2 norm) is developed. As its application, this method is employed to perform seismic waveform inversions — Model 1, for a homogeneous isotropic earth with a 2-D rectangle embedded body, and Model 2, for a layered earth with an elliptically elongated inclusion. A fast computation algorithm of the finite element method is adopted to generate a series of synthetic shot records for training the 3-layer neural network. The trained neural network possesses the capability to find the acoustic velocity of the embedded body in both Model 1 and 2 with a real-time solution within a sufficient accuracy.

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3

Saad, Emad W., and Donald C. Wunsch. "Neural network explanation using inversion." Neural Networks 20, no. 1 (January 2007): 78–93. http://dx.doi.org/10.1016/j.neunet.2006.07.005.

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4

Sonehara, Noboru, and Yukio Tokunaga. "Neural Network Models for Image Inversion." Journal of Robotics and Mechatronics 5, no. 2 (April 20, 1993): 88–97. http://dx.doi.org/10.20965/jrm.1993.p0088.

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5

Das, Vishal, Ahinoam Pollack, Uri Wollner, and Tapan Mukerji. "Convolutional neural network for seismic impedance inversion." GEOPHYSICS 84, no. 6 (November 1, 2019): R869—R880. http://dx.doi.org/10.1190/geo2018-0838.1.

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We have addressed the geophysical problem of obtaining an elastic model of the subsurface from recorded normal-incidence seismic data using convolutional neural networks (CNNs). We train the network on synthetic full-waveform seismograms generated using Kennett’s reflectivity method on earth models that were created under rock-physics modeling constraints. We use an approximate Bayesian computation method to estimate the posterior distribution corresponding to the CNN prediction and to quantify the uncertainty related to the predictions. In addition, we test the robustness of the network in predicting impedances of previously unobserved earth models when the input to the network consisted of seismograms generated using: (1) earth models with different spatial correlations (i.e. variograms), (2) earth models with different facies proportions, (3) earth models with different underlying rock-physics relations, and (4) source-wavelet phase and frequency different than in the training data. Results indicate that the predictions of the trained network are susceptible to facies proportions, the rock-physics model, and source-wavelet parameters used in the training data set. Finally, we apply CNN inversion on the Volve field data set from offshore Norway. P-wave impedance [Formula: see text] inverted for the Volve data set using CNN showed a strong correlation (82%) with the [Formula: see text] log at a well.

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6

Zhu, Weiqiang, Kailai Xu, Eric Darve, Biondo Biondi, and Gregory C. Beroza. "Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification." GEOPHYSICS 87, no. 1 (December 6, 2021): R93—R109. http://dx.doi.org/10.1190/geo2020-0933.1.

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Full-waveform inversion (FWI) is an accurate imaging approach for modeling the velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We have adopted a neural-network-based full-waveform inversion (NNFWI) method that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. The velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of the neural networks and PDEs are calculated using automatic differentiation, which back propagates gradients through the acoustic PDEs and neural network layers to update the weights of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model determine that NNFWI can mitigate local minima, especially for imaging high-contrast features such as salt bodies, and it significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.

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7

Yu, Ran Gang, and Yong Tian. "Application of Hybrid Genetic Algorithm in Ground Stress Inversion." Applied Mechanics and Materials 90-93 (September 2011): 337–41. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.337.

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This paper propose genetic algorithm combined with neural networks, greatly improving the convergence rate of neural network aim at the disadvantage of the traditional BP neural network inversion method is easy to fall into local minimum and slow convergence.Finally, verified the feasibility and superiority of the above methods through the successful initial ground stress inversion of actual project.

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8

Živković, Ivan S., Predrag S. Stanimirović, and Yimin Wei. "Recurrent Neural Network for Computing Outer Inverse." Neural Computation 28, no. 5 (May 2016): 970–98. http://dx.doi.org/10.1162/neco_a_00821.

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Two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined. Each of the proposed recurrent neural networks is based on the matrix-valued differential equation, a generalization of dynamic equations proposed earlier for the nonsingular matrix inversion, the Moore-Penrose inversion, as well as the Drazin inversion, under the condition of zero initial state. The application of the first approach is conditioned by the properties of the spectrum of a certain matrix; the second approach eliminates this drawback, though at the cost of increasing the number of matrix operations. The cases corresponding to the most common generalized inverses are defined. The conditions that ensure stability of the proposed neural network are presented. Illustrative examples present the results of numerical simulations.

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9

Milić, I., and R. Gafeira. "Mimicking spectropolarimetric inversions using convolutional neural networks." Astronomy & Astrophysics 644 (December 2020): A129. http://dx.doi.org/10.1051/0004-6361/201936537.

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Context. Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or “inversion”, used to infer physical quantities from the observations is extremely slow, because the underlying models are numerically demanding. Aims. We aim to improve the speed of the inference by using a neural network that relates input polarized spectra to the output physical parameters. Methods. We first select a subset of the data to be interpreted and infer physical quantities from corresponding spectra using a standard minimization-based inversion code. Taking these results as reliable and representative of the whole data set, we train a convolutional neural network to connect the input polarized spectra to the output physical parameters (nodes, in context of spectropolarimetric inversion). We then apply the neural network to the various other data, previously unseen to the network. As a check, we apply the referent inversion code to the unseen data and compare the fit quality and the maps of the inferred parameters between the two inversions. Results. The physical parameters inferred by the neural network show excellent agreement with the results from the inversion, and are obtained in a factor of 105 less time. Additionally, substituting the results of the neural network back in the forward model, shows excellent agreement between inferred and original spectra. Conclusions. The method we present here is very simple for implementation and extremely fast. It only requires a training data set, which can be obtained by inverting a representative subset of the observed data. Applying these (and similar) machine learning techniques will yield orders of magnitude acceleration in the routine interpretation of spectropolarimetric data.

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10

Mohamed, Islam A., Hamed Z. El-Mowafy, and Mohamed Fathy. "Prediction of elastic properties using seismic prestack inversion and neural network analysis." Interpretation 3, no. 2 (May 1, 2015): T57—T68. http://dx.doi.org/10.1190/int-2014-0139.1.

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The use of artificial intelligence algorithms to solve geophysical problems is a recent development. Neural network analysis is one of these algorithms. It uses the information from multiple wells and seismic data to train a neural network to predict properties away from the well control. Neural network analysis can significantly improve the seismic inversion result when the outputs of the inversion are used as external attributes in addition to regular seismic attributes for training the network. We found that integration of prestack inversion and neural network analysis can improve the characterization of a late Pliocene gas sandstone reservoir. For inversion, the input angle stacks was conditioned to match the theoretical amplitude-variation-with-offset response. The inversion was performed using a deterministic wavelet set. Neural network analysis was then used to enhance the [Formula: see text], [Formula: see text], and density volumes from the inversion. The improvement was confirmed by comparisons with logs from a blind well.

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11

Fa-Long, Luo, and Bao Zheng. "Neural network approach to computing matrix inversion." Applied Mathematics and Computation 47, no. 2-3 (February 1992): 109–20. http://dx.doi.org/10.1016/0096-3003(92)90040-8.

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12

Elkattan, Mohamed, and Aladin H. Kamel. "Estimation of Electromagnetic Properties for 2D Inhomogeneous Media Using Neural Networks." Journal of Electromagnetic Engineering and Science 22, no. 2 (March 31, 2022): 152–61. http://dx.doi.org/10.26866/jees.2022.2.r.72.

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Electromagnetic measurements are widely used to gain information about an object through interaction of electromagnetic fields with the physical properties of this object. The inversion problem is the process of estimating object parameters from electromagnetic records. This problem has a nonlinear nature and can be formulated as an optimization scheme. In this paper, we introduce an inversion methodology to estimate the electrical properties of a two-dimensional inhomogeneous layered scattering object. The proposed methodology deals with the inversion problem as a learning process through two multilayer perceptron artificial neural network designs. Several neural network design parameters were tuned to achieve the best inversion performance. Moreover, the proposed neural networks were tested against noise presence in terms of error criteria and proved to be effective in solving the inverse scattering problem.

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13

Liu, Wen Ming, Wan Jin Liu, Hong Wei Wang, and Xin Zhang. "Research on Multi-Attributes Neural Network Inversion in Coalmines’ 3D Seismic Exploration." Applied Mechanics and Materials 556-562 (May 2014): 5539–43. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.5539.

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The conventional inversion can only get P-impedance data, but neural network inversion can obtain various kinds of well-log attributes data by getting the nonlinear relationship through training the data of seismic attributes and well-log attributes, and then apply the nonlinear relationship to the whole seismic data volume. In this paper, we use multilayer feed forward neural network, probability neural network and radial basis function neural network to carry out the log-density inversion research, and obtain three pseudo density data volumes. We compare the effect of the inversion results and analysis the density distribution in spatial domain through section and slice data, at last we predict the stability of the coal seam’s floor in more reasonable way.

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14

Shimabukuro, Hayato, and Benoit Semelin. "Analysing 21cm signal with artificial neural network." Proceedings of the International Astronomical Union 12, S333 (October 2017): 39–42. http://dx.doi.org/10.1017/s174392131701081x.

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AbstractThe 21cm signal at epoch of reionization (EoR) should be observed within next decade. We expect that cosmic 21cm signal at the EoR provides us both cosmological and astrophysical information. In order to extract fruitful information from observation data, we need to develop inversion method. For such a method, we introduce artificial neural network (ANN) which is one of the machine learning techniques. We apply the ANN to inversion problem to constrain astrophysical parameters from 21cm power spectrum. We train the architecture of the neural network with 70 training datasets and apply it to 54 test datasets with different value of parameters. We find that the quality of the parameter reconstruction depends on the sensitivity of the power spectrum to the different parameter sets at a given redshift and also find that the accuracy of reconstruction is improved by increasing the number of given redshifts. We conclude that the ANN is viable inversion method whose main strength is that they require a sparse extrapolation of the parameter space and thus should be usable with full simulation.

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15

Boadu, Fred K. "Inversion of fracture density from field seismic velocities using artificial neural networks." GEOPHYSICS 63, no. 2 (March 1998): 534–45. http://dx.doi.org/10.1190/1.1444354.

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The inversion of fracture density from field measured P- and S-wave seismic velocities is performed using a neural network trained with an output from the modified displacement discontinuity fracture model. The basic idea is to use input‐output pairs generated by the fracture model to train the neural network. Once the neural network is trained, inversion of fracture density from field‐measured seismic velocities is performed very quickly. The overall performance of the neural network in the inversion process is assessed by means of a loss function. The results indicate that both sources of field information (P- and S-wave velocities) predict the field fracture density with reasonable accuracy. The performance of the neural network was compared to the prediction from least‐squares fitting. It is shown that the neural network out performs the least‐squares fitting in predicting the field‐fracture density values.

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Baddari, Kamel, Noureddine Djarfour, Tahar Aïfa, and Jalal Ferahtia. "Acoustic impedance inversion by feedback artificial neural network." Journal of Petroleum Science and Engineering 71, no. 3-4 (April 2010): 106–11. http://dx.doi.org/10.1016/j.petrol.2009.09.012.

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17

Najnin, Shamima, and Bonny Banerjee. "Improved speech inversion using general regression neural network." Journal of the Acoustical Society of America 138, no. 3 (September 2015): EL229—EL235. http://dx.doi.org/10.1121/1.4929626.

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18

Rodriguez, Alberto F., William E. Blass, John H. Missimer, and Klaus L. Leenders. "Artificial neural network Radon inversion for image reconstruction." Medical Physics 28, no. 4 (April 2001): 508–14. http://dx.doi.org/10.1118/1.1357222.

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19

Wu, Yulang, and George A. McMechan. "Parametric convolutional neural network-domain full-waveform inversion." GEOPHYSICS 84, no. 6 (November 1, 2019): R881—R896. http://dx.doi.org/10.1190/geo2018-0224.1.

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Most current full-waveform inversion (FWI) algorithms minimize the data residuals to estimate a velocity model based on the assumption that the updated model is the sum of a background model and an estimated model perturbation. We have performed reparameterization of the initial velocity model, by the weights in a convolutional neural network (CNN), to automatically capture the salient features in the initial model, as a priori information. The prior information in CNN weights is iteratively updated as regularization to constrain the CNN-domain inversion to refine the features captured in CNN pretraining by reducing the data misfit. Synthetic examples using a 1D increasing velocity function v(z) and a 2D smoothed version of the correct Marmousi2 model as initial models indicate that the performance of the CNN-domain FWI depends on the existence and accuracy of the prior information in the initial velocity model (i.e., whether features whose positions, shapes, and values are present in the correct model are approximately included in the initial model). Forty different sets of randomly initialized CNN weights are used to parameterize and test CNN-domain FWI, using a 2D smoothed Sigsbee model as the initial velocity model. All 40 sets invert for the Sigsbee salt body more accurately (with a smaller standard deviation of the final rms model errors), by CNN-domain FWI, than FWI does. Features that are not represented within the CNN hidden layers in the initial velocity model, and so cannot be recovered by CNN-domain FWI, can be recovered using the final CNN-domain FWI velocity model as the starting model in a subsequent conventional FWI.

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20

Adam, Stavros P., Aristidis C. Likas, and Michael N. Vrahatis. "Evaluating generalization through interval-based neural network inversion." Neural Computing and Applications 31, no. 12 (March 22, 2019): 9241–60. http://dx.doi.org/10.1007/s00521-019-04129-5.

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21

Al-Garni, Mansour A. "Inversion of residual gravity anomalies using neural network." Arabian Journal of Geosciences 6, no. 5 (November 22, 2011): 1509–16. http://dx.doi.org/10.1007/s12517-011-0452-y.

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22

Yin, Lirong, Lei Wang, Weizheng Huang, Jiawei Tian, Shan Liu, Bo Yang, and Wenfeng Zheng. "Haze Grading Using the Convolutional Neural Networks." Atmosphere 13, no. 4 (March 25, 2022): 522. http://dx.doi.org/10.3390/atmos13040522.

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As an air pollution phenomenon, haze has become one of the focuses of social discussion. Research into the causes and concentration prediction of haze is significant, forming the basis of haze prevention. The inversion of Aerosol Optical Depth (AOD) based on remote sensing satellite imagery can provide a reference for the concentration of major pollutants in a haze, such as PM2.5 concentration and PM10 concentration. This paper used satellite imagery to study haze problems and chose PM2.5, one of the primary haze pollutants, as the research object. First, we used conventional methods to perform the inversion of AOD on remote sensing images, verifying the correlation between AOD and PM2.5. Subsequently, to simplify the parameter complexity of the traditional inversion method, we proposed using the convolutional neural network instead of the traditional inversion method and constructing a haze level prediction model. Compared with traditional aerosol depth inversion, we found that convolutional neural networks can provide a higher correlation between PM2.5 concentration and satellite imagery through a more simplified satellite image processing process. Thus, it offers the possibility of researching and managing haze problems based on neural networks.

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23

Zhang, Yongsheng, Lin Xiao, Lei Ding, Zhiguo Tan, KE Chenc, and Yumin Yina. "Design of a nonlinearly activated gradient-based neural network and its application to matrix inversion." Filomat 34, no. 15 (2020): 5095–101. http://dx.doi.org/10.2298/fil2015095z.

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Different from the traditional linearly activated gradient-based neural network model (GNN model), two nonlinear activation functions are presented and investigated to construct two nonlinear gradient-based neural network models (NGNN-1 model and NGNN-2 model) for matrix inversion in this paper. For comparative and illustrative purposes, the traditional GNN model is also used to solve matrix inversion problems under the same circumstance. In addition, the simulation results of the computer finally confirm the validity and superiority of the two nonlinear gradient-based neural network models specially activated by two nonlinear activation functions for matrix inversion, as compared with the traditional GNN model.

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24

Kushnir, Dmitry Yu, Nikolay N. Velker, Darya V. Andornaya, and Yuriy E. Antonov. "NEURAL NETWORK INVERSION OF RESISTIVITY DATA FOR DETERMINATION OF DISTANCE TO A BED BOUNDARY." Interexpo GEO-Siberia 2, no. 2 (May 21, 2021): 95–102. http://dx.doi.org/10.33764/2618-981x-2021-2-2-95-102.

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Accurate real-time estimation of a distance to the nearest bed boundary simplifies the steering of directional wells. For estimation of that distance, we propose an approach of pointwise inversion of resistivity data using neural networks based on two-layer resistivity formation model. The model parameters are determined from the tool responses using a cascade of neural networks. The first network calculates the resistivity of the layer containing the tool measure point. The subsequent networks take as input the tool responses and the model parameters determined with the previous networks. All networks are trained on the same synthetic database. The samples of that database consist of the pairs of model parameters and corresponding noisy tool responses. The results of the proposed approach are close to the results of the general inversion algorithm based on the method of the most-probable parameter combination. At the same time, the performance of the proposed inversion is several orders faster.

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25

Lei, Feng, You Yu, Daijun Zhang, Li Feng, Jinsong Guo, Yong Zhang, and Fang Fang. "Water remote sensing eutrophication inversion algorithm based on multilayer convolutional neural network." Journal of Intelligent & Fuzzy Systems 39, no. 4 (October 21, 2020): 5319–27. http://dx.doi.org/10.3233/jifs-189017.

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In recent years, with the rapid development of satellite technology, remote sensing inversion has been used as an important part of environmental monitoring. Remote sensing inversion has been prepared for large-scale water environment monitoring in the watershed that is difficult for the traditional water environment monitoring methods. This paper will discuss some shortcomings of traditional remote sensing inversion methods, and proposes a remote sensing inversion method based on convolutional neural network, which realizes large-scale remote sensing smart and automatic inversion monitoring of the water environment. The results show that the method is practical and effective, and can achieve high recognition accuracy for water blooms.

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Wang, X. K., H. Zhao, H. L. Zhang, Y. P. Liu, and C. Shu. "RESEARCH ON INVERSION OF LIDAR EQUATION BASED ON NEURAL NETWORK." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3/W9 (October 25, 2019): 171–76. http://dx.doi.org/10.5194/isprs-archives-xlii-3-w9-171-2019.

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Abstract. Lidar is an advanced atmospheric and meteorological monitoring instrument. The atmospheric aerosol physical parameters can be acquired through inversion of lidar signals. However, traditional methods of solving lidar equations require many assumptions and cannot get accurate analytical solutions. In order to solve this problem, a method of inverting lidar equation using artificial neural network is proposed. This method is based on BP (Back Propagation) artificial neural network, the weights and thresholds of BP artificial neural network is optimized by Genetic Algorithm. The lidar equation inversion prediction model is established. The actual lidar detection signals are inversed using this method, and the results are compared with the traditional method. The result shows that the extinction coefficient and backscattering coefficient inverted by the GA-based BP neural network model are accurate than that inverted by traditional method, the relative error is below 4%. This method can solve the problem of complicated calculation process, as while as providing a new method for the inversion of lidar equations.

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27

Shahraeeni, Mohammad S., and Andrew Curtis. "Fast probabilistic nonlinear petrophysical inversion." GEOPHYSICS 76, no. 2 (March 2011): E45—E58. http://dx.doi.org/10.1190/1.3540628.

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We have developed an extension of the mixture-density neural network as a computationally efficient probabilistic method to solve nonlinear inverse problems. In this method, any postinversion (a posteriori) joint probability density function (PDF) over the model parameters is represented by a weighted sum of multivariate Gaussian PDFs. A mixture-density neural network estimates the weights, mean vector, and covariance matrix of the Gaussians given any measured data set. In one study, we have jointly inverted compressional- and shear-wave velocity for the joint PDF of porosity, clay content, and water saturation in a synthetic, fluid-saturated, dispersed sand-shale system. Results show that if the method is applied appropriately, the joint PDF estimated by the neural network is comparable to the Monte Carlo sampled a posteriori solution of the inverse problem. However, the computational cost of training and using the neural network is much lower than inversion by sampling (more than a factor of 104 in this case and potentially a much larger factor for 3D seismic inversion). To analyze the performance of the method on real exploration geophysical data, we have jointly inverted P-wave impedance and Poisson’s ratio logs for the joint PDF of porosity and clay content. Results show that the posterior model PDF of porosity and clay content is a good estimate of actual porosity and clay-content log values. Although the results may vary from one field to another, this fast, probabilistic method of solving nonlinear inverse problems can be applied to invert well logs and large seismic data sets for petrophysical parameters in any field.

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Hardman, Rachael L., and Lucy R. Wyatt. "Inversion of HF Radar Doppler Spectra Using a Neural Network." Journal of Marine Science and Engineering 7, no. 8 (August 6, 2019): 255. http://dx.doi.org/10.3390/jmse7080255.

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For a number of decades, coastal HF radar has been used to remotely measure ocean surface parameters, including waves, at distances exceeding 100 km. The information, which has value in many ocean engineering applications, is obtained using the HF radar cross-section, which relates the directional ocean spectrum to the received radar signal, through a nonlinear integral equation. The equation is impossible to solve analytically, for the ocean spectrum, and a number of numerical methods are currently used. In this study, a neural network is trained to infer the directional ocean spectrum from HF radar Doppler spectra. The neural network is trained and tested on simulated radar data and then validated with data collected off the coast of Cornwall, where there are two HF radars and a wave buoy to provide the sea-truth. Key ocean parameters are derived from the estimated directional spectra and then compared with the values measured by both the wave buoy and an existing inversion method. The results are encouraging; for example, the RMSE of the obtained mean wave direction decreases from 20.6° to 15.7°. The positive results show that neural networks may be a viable solution in certain situations, where existing methods struggle.

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Wang, Shengchao, Liguo Han, Xiangbo Gong, Shaoyue Zhang, Xingguo Huang, and Pan Zhang. "MCMC Method of Inverse Problems Using a Neural Network—Application in GPR Crosshole Full Waveform Inversion: A Numerical Simulation Study." Remote Sensing 14, no. 6 (March 9, 2022): 1320. http://dx.doi.org/10.3390/rs14061320.

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Ground-penetrating radar (GPR) crosshole tomography is widely applied to subsurface media images. However, the inadequacies of ray methods may limit the resolution of crosshole radar images, since the ray method is a type of high-frequency approximation. To solve this problem, the full waveform method is introduced for GPR inversion. However, full waveform inversion is computationally expensive. In this paper, we introduce a trained neural network that can be evaluated very quickly to replace a computationally intensive forward model. Additionally, the forward error of the trained neural network can be statistically analyzed. We demonstrate a methodology for a full waveform inversion of crosshole ground-penetrating radar data using the Markov chain Monte Carlo (MCMC) method. An accurate forward model based on Maxwell’s equations is replaced by a quickly trained neural network. This method achieves a high computation efficiency, which is four orders of magnitude faster than the accurate forward model. The inversion result of the synthetic waveform data shows a good performance of the trained neural network, which greatly improves the calculation efficiency.

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30

He, Qinglong, and Yanfei Wang. "Reparameterized full-waveform inversion using deep neural networks." GEOPHYSICS 86, no. 1 (December 14, 2020): V1—V13. http://dx.doi.org/10.1190/geo2019-0382.1.

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Full-waveform inversion (FWI) is a powerful method for providing a high-resolution description of the subsurface. However, the misfit function of the conventional FWI method (metric [Formula: see text]-norm) is usually dominated by spurious local minima owing to its nonlinearity and ill-posedness. In addition, FWI requires intensive wavefield computation to evaluate the gradient and step length. We have considered a general inversion method using a deep neural network (DNN) for the FWI problem. This deep-learning inversion method reparameterizes physical parameters using the weights of a DNN, such that the inversion amounts to reconstructing these weights. One advantage of this deep-learning inversion method is that it can serve as an iterative regularization method, benefiting from the representation of the network. Thus, it is suitable to solve ill-posed nonlinear inverse problems. Furthermore, this method possesses good computational efficiency because it only requires first-order derivatives. In addition, it can easily be accelerated by using multiple graphics processing units and central processing units, for weight updating and forward modeling. Synthetic experiments, based on the Marmousi2, 2004 BP, and a metal ore model, are used to show the numerical performance of the deep-learning inversion method. Comprehensive comparisons with a total-variation regularized FWI are presented to show the ability of our method to recover sharp boundaries. Our numerical results indicate that this deep-learning inversion approach is effective, efficient, and can capture salient features of the model.

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31

Xiao, Chang Lin, Yan Chen, Lina Liu, Ling Tong, and Ming Quan Jia. "Soil Moisture Retrieval Based on ASAR Data and Genetic Neural Networks." Key Engineering Materials 500 (January 2012): 198–203. http://dx.doi.org/10.4028/www.scientific.net/kem.500.198.

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Genetic Algorithm can further optimize Neural Networks, and this optimized Algorithm has been used in many fields and made better results, but currently, it have not been used in inversion parameters. This paper used backscattering coefficients from ASAR, AIEM model to calculate data as neural network training data and through Genetic Algorithm Neural Networks to retrieve soil moisture. Finally compared with practical test and shows the validity and superiority of the Genetic Algorithm Neural Networks.

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32

Guo, Qiaozhen, Huanhuan Wu, Huiyi Jin, Guang Yang, and Xiaoxu Wu. "Remote Sensing Inversion of Suspended Matter Concentration Using a Neural Network Model Optimized by the Partial Least Squares and Particle Swarm Optimization Algorithms." Sustainability 14, no. 4 (February 15, 2022): 2221. http://dx.doi.org/10.3390/su14042221.

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Suspended matter concentration is an important index for the assessment of a water environment and it is also one of the core parameters for remote sensing inversion of water color. Due to the optical complexity of a water body and the interaction between different water quality parameters, the remote sensing inversion accuracy of suspended matter concentration is currently limited. To solve this problem, based on the remote sensing images from Gaofen-2 (GF-2) and the field-measured suspended matter concentration, taking a section of the Haihe River as the study area, this study establishes a remote sensing inversion model. The model combines the partial least squares (PLS) algorithm and the particle swarm optimization (PSO) algorithm to optimize the back-propagation neural network (BPNN) model, i.e., the PLS-PSO-BPNN model. The partial least squares algorithm is involved in screening the input values of the neural network model. The particle swarm optimization algorithm optimizes the weights and thresholds of the neural network model and it thus effectively overcomes the over-fitting of the neural network. The inversion accuracy of the optimized neural network model is compared with that of the partial least squares model and the traditional neural network model by determining the coefficient, the mean absolute error, the root mean square error, the correlation coefficient and the relative root mean square error. The results indicate that the root mean squared error of the PLS-PSO-BPNN inversion model was 3.05 mg/L, which is higher than the accuracy of the statistical regression model. The developed PLS-PSO-BPNN model could be widely applied in other areas to better invert the water quality parameters of surface water.

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33

Li, Xiao Li, and Zhao Long Yin. "Inversion Analysis on the Initial Damage of Concrete." Applied Mechanics and Materials 543-547 (March 2014): 4048–51. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.4048.

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The inverse analysis method based on genetic algorithm has been widely applied, but the general genetic algorithm is not applicable to the objective function as a non-analytic formula, so that the clear target function formula is often difficultly been obtained in the practical engineering. In order to solve the problem, the historical data are studied by neural network with the neural network embedded into the genetic algorithm, so as to establish the effective neural network model to replace the target function formula. At the same time, the corresponding fitness function is constructed for the optimal calculation. This method has been used for the inversion analysis on the initial damage of concrete, and the mechanical parameter inversion method is put forward based on the uniform design-genetic algorithm-neural network ensemble theory. Moreover, the method is verified by a calculation example, the results show that the initial damage value of concrete can effectively be obtained.

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34

LEEF, JEONG-WOO, and JUN-HO OHT. "Inversion of multilayer neural network with modelling error compensation." International Journal of Systems Science 28, no. 8 (July 1997): 817–30. http://dx.doi.org/10.1080/00207729708929442.

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35

Lee, J. W., and J. H. Oh. "Inversion control of nonlinear systems with neural network modelling." IEE Proceedings - Control Theory and Applications 144, no. 5 (September 1, 1997): 481–87. http://dx.doi.org/10.1049/ip-cta:19971360.

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36

Too, Gee‐Pinn, and Suzi Hwang. "Inversion for acoustic impedance using artificial neural network algorithm." Journal of the Acoustical Society of America 114, no. 4 (October 2003): 2324. http://dx.doi.org/10.1121/1.4780994.

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37

Katsakos, D., C. Panchev, and I. Marinova. "A neural network inversion approach to electromagnetic device design." IEEE Transactions on Magnetics 36, no. 4 (July 2000): 1080–84. http://dx.doi.org/10.1109/20.877628.

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38

Pedro, J. O., and N. D. Meyer. "NEURAL NETWORK-BASED DYNAMIC INVERSION CONTROLLER FOR FIGHTER AIRCRAFTS." IFAC Proceedings Volumes 40, no. 12 (2007): 946–51. http://dx.doi.org/10.3182/20070822-3-za-2920.00157.

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39

Fu, Hongsun, Yan Zhang, and Mingyue Ma. "Seismic waveform inversion using a neural network-based forward." Journal of Physics: Conference Series 1324 (October 2019): 012043. http://dx.doi.org/10.1088/1742-6596/1324/1/012043.

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40

XU, Hai-Lang, and Xiao-Ping WU. "2-D Resistivity Inversion Using the Neural Network Method." Chinese Journal of Geophysics 49, no. 2 (March 2006): 507–14. http://dx.doi.org/10.1002/cjg2.861.

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41

Wang, Jun. "A recurrent neural network for real-time matrix inversion." Applied Mathematics and Computation 55, no. 1 (April 1993): 89–100. http://dx.doi.org/10.1016/0096-3003(93)90007-2.

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42

Mann, J. M., L. W. Schmerr, and J. C. Moulder. "Neural network inversion of uniform-field eddy current data." NDT & E International 25, no. 1 (January 1992): 43. http://dx.doi.org/10.1016/0963-8695(92)90071-n.

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43

Koponen, Janne, Timo Lähivaara, Jari Kaipio, and Marko Vauhkonen. "Model reduction in acoustic inversion by artificial neural network." Journal of the Acoustical Society of America 150, no. 5 (November 2021): 3435–44. http://dx.doi.org/10.1121/10.0007049.

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44

Stephan, Yann, Xavier Demoulin, and Olivier Sarzeaud. "Neural Direct Approaches for Geoacoustic Inversion." Journal of Computational Acoustics 06, no. 01n02 (March 1998): 151–66. http://dx.doi.org/10.1142/s0218396x98000120.

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This paper presents different neural network approaches for geoacoustic inversion. The basic idea of neural inversion is to approximate the inverse function from a set of behaviors, i.e. relations between acoustic fields and geoacoustic parameters. In this work, such methods have been applied in two different forms: a global approach which aims to estimate all parameters from all data, and a hierarchical approach in which the most sensitive parameters are estimated before the least sensitive. The methods are tested using synthetic data. Statistical results, as well as benchmark results show that such approaches are efficient and have similar performances.

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45

Alfarraj, Motaz, and Ghassan AlRegib. "Semisupervised sequence modeling for elastic impedance inversion." Interpretation 7, no. 3 (August 1, 2019): SE237—SE249. http://dx.doi.org/10.1190/int-2018-0250.1.

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Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints — the lack of which might lead to undesirable results. To overcome this issue, we have developed a semisupervised sequence modeling framework based on recurrent neural networks for elastic impedance inversion from multiangle seismic data. Specifically, seismic traces and elastic impedance (EI) traces are modeled as a time series. Then, a neural-network-based inversion model comprising convolutional and recurrent neural layers is used to invert seismic data for EI. The proposed workflow uses well-log data to guide the inversion. In addition, it uses seismic forward modeling to regularize the training and to serve as a geophysical constraint for the inversion. The proposed workflow achieves an average correlation of 98% between the estimated and target EI using 10 well logs for training on a synthetic data set.

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46

Yang, Cheng Zhong, and Xian Da Xu. "Intelligent Identification of High Rock-Filled Embankment Constitutive Model Parameters." Advanced Materials Research 183-185 (January 2011): 2139–42. http://dx.doi.org/10.4028/www.scientific.net/amr.183-185.2139.

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Based on the orthogonal design method, the finite element method was combined with the artificial neural network to have established high rock-filled embankment constitutive model parameters inverse analysis method. According to orthogonal design requirements, the level of inversion parameters were selected and the numerical simulation program were determined. By ANSYS software calculated out the analysis samples of neural network and trained the BP neural network.Using the field monitoring displacement,the soil constitutive model parameters were identified and the inversion parameters were compared with the theoretical value.The results show that: the maximum relative error of the inversion value with the theoretical value is no more than 9%,which meets accuracy requirements.

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47

Liao, Bolin, Lin Xiao, Jie Jin, Lei Ding, and Mei Liu. "Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 1 (January 19, 2016): 132–38. http://dx.doi.org/10.20965/jaciii.2016.p0132.

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Static matrix inverse solving has been studied for many years. In this paper, we aim at solving a dynamic complex-valued matrix inverse. Specifically, based on the artful combination of a conventional gradient neural network and the recently-proposed Zhang neural network, a novel complex-valued neural network model is presented and investigated for computing the dynamic complex-valued matrix inverse in real time. A hardware implementation structure is also offered. Moreover, both theoretical analysis and simulation results substantiate the effectiveness and advantages of the proposed recurrent neural network model for dynamic complex-valued matrix inversion.

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48

Cheng, Xianqiong, Qihe Liu, Pingping Li, and Yuan Liu. "Inverting Rayleigh surface wave velocities for crustal thickness in eastern Tibet and the western Yangtze craton based on deep learning neural networks." Nonlinear Processes in Geophysics 26, no. 2 (April 17, 2019): 61–71. http://dx.doi.org/10.5194/npg-26-61-2019.

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Abstract. Crustal thickness is an important factor affecting lithospheric structure and deep geodynamics. In this paper, a deep learning neural network based on a stacked sparse auto-encoder is proposed for the inversion of crustal thickness in eastern Tibet and the western Yangtze craton. First, with the phase velocity of the Rayleigh surface wave as input and the theoretical crustal thickness as output, 12 deep-sSAE neural networks are constructed, which are trained by 380 000 and tested by 120 000 theoretical models. We then invert the observed phase velocities through these 12 neural networks. According to the test error and misfit of other crustal thickness models, the optimal crustal thickness model is selected as the crustal thickness of the study area. Compared with other ways to detect crustal thickness such as seismic wave reflection and receiver function, we adopt a new way for inversion of earth model parameters, and realize that a deep learning neural network based on data driven with the highly non-linear mapping ability can be widely used by geophysicists, and our result has good agreement with high-resolution crustal thickness models. Compared with other methods, our experimental results based on a deep learning neural network and a new Rayleigh wave phase velocity model reveal some details: there is a northward-dipping Moho gradient zone in the Qiangtang block and a relatively shallow north-west–south-east oriented crust at the Songpan–Ganzi block. Crustal thickness around Xi'an and the Ordos basin is shallow, about 35 km. The change in crustal thickness in the Sichuan–Yunnan block is sharp, where crustal thickness is 60 km north-west and 35 km south-east. We conclude that the deep learning neural network is a promising, efficient, and believable geophysical inversion tool.

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49

Xin, Gong Cai, Wei Lun Chen, and Jin Niu Tao. "Design of Neutral Network–Sliding Model Based Large Envelope Flight Control Law." Advanced Materials Research 532-533 (June 2012): 503–7. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.503.

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Applying neutral network-sliding model control design methods to large envelope flight control law of aircraft whose model parameter varies greatly with flight condition was studied in this paper. Neural network theory is used to approximately linearize the nonlinear system and cancel the errors brought with approximate inversion, and the residual error is solved by sliding model control. So it can approximate the nonlinear model accurately, and improve robustness and anti-jamming capability of the flight control system. Simulation results show the design neural network – sliding model large envelope flight controller has excellent control performance.

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50

Zhang, Zhiyi, and Zhiqiang Zhou. "Real time quasi–2-D inversion of array resistivity logging data using neural network." GEOPHYSICS 67, no. 2 (March 2002): 517–24. http://dx.doi.org/10.1190/1.1468612.

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We present a quasi-2-D real-time inversion algorithm for a modern galvanic array tool via dimensional reduction and neural network simulation. Using reciprocity and superposition, we apply a numerical focusing technique to the unfocused data. The numerically focused data are much less subject to 2-D and layering effects and can be approximated as from a cylindrical 1-D earth. We then perform 1-D inversion on the focused data to provide approximate information about the 2-D resistivity structure. A neural network is used to perform forward modeling in the 1-D inversion, which is several hundred times faster than conventional numerical forward solutions. Testing our inversion algorithm on both synthetic and field data shows that this fast inversion algorithm is useful for providing formation resistivity information at a well site.

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