WAVEFORM INVERSION AND MULTI-LAYER NEURAL NETWORK

1995 ◽  
Vol 03 (03) ◽  
pp. 175-202 ◽  
Author(s):  
DONGYU FEI ◽  
JOHN T. KUO ◽  
YU-CHIUNG TENG
Keyword(s):  
Neural Network ◽  
Continuous Function ◽  
Mathematical Problem ◽  
Initial Guess ◽  
Acoustic Velocity ◽  
Inversion Method ◽  
True Parameter ◽  
Seismic Waveform ◽  
Neural Network Inversion ◽  
The Neural Network

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.

scholarly journals Analysing 21cm signal with artificial neural network

2017 ◽  
Vol 12 (S333) ◽  
pp. 39-42
Author(s):  
Hayato Shimabukuro ◽  
Benoit Semelin
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Power Spectrum ◽  
Machine Learning Techniques ◽  
Inversion Method ◽  
Observation Data ◽  
The Neural Network ◽  
Learning Techniques ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

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.

Application of Hybrid Genetic Algorithm in Ground Stress Inversion

2011 ◽  
Vol 90-93 ◽  
pp. 337-341
Author(s):  
Ran Gang Yu ◽  
Yong Tian
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Neural Networks ◽  
Bp Neural Network ◽  
Local Minimum ◽  
Hybrid Genetic Algorithm ◽  
Inversion Method ◽  
Stress Inversion ◽  
Neural Network Inversion ◽  
Ground Stress

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.

scholarly journals The Construction and Approximation of the Neural Network with Two Weights

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiyong Quan ◽  
Zhengqiu Zhang
Keyword(s):  
Neural Network ◽  
Fourier Series ◽  
Continuous Function ◽  
Bp Neural Network ◽  
Partition Of Unity ◽  
Sigmoidal Functions ◽  
The Neural Network ◽  
Inequality Technique ◽  
The Way

The technique of approximate partition of unity, the way of Fourier series, and inequality technique are used to construct a neural network with two weights and with sigmoidal functions. Furthermore by using inequality technique, we prove that the neural network with two weights can more precisely approximate any nonlinear continuous function than BP neural network constructed in (Chen et al., 2012).

scholarly journals Combined neural network/Phillips-Tikhonov approach to aerosol retrievals over land from the NASA Research Scanning Polarimeter

2017 ◽  
Author(s):  
Antonio Di Noia ◽  
Otto P. Hasekamp ◽  
Lianghai Wu ◽  
Bastiaan van Diedenhoven ◽  
Brian Cairns ◽  
...  
Keyword(s):  
Neural Network ◽  
Land Surface ◽  
Processing Time ◽  
Iterative Scheme ◽  
Initial Guess ◽  
Effective Radius ◽  
Aerosol Layer ◽  
Large Dataset ◽  
The Neural Network ◽  
Fine Mode

Abstract. In this paper, an algorithm for the retrieval of aerosol and land surface properties from airborne spectropolarimetric measurements – combining neural networks and an iterative scheme based on Phillips-Tikhonov regularization – is described. The algorithm – which is an extension of a scheme previously designed for ground-based retrievals – is applied to measurements from the Research Scanning Polarimeter (RSP) onboard the NASA ER-2 aircraft. A neural network, trained on a large dataset of synthetic measurements, is applied to perform aerosol retrievals from real RSP data, and the neural network retrievals are subsequently used as first guess for the Phillips-Tikhonov retrieval. The resulting algorithm appears capable of accurately retrieving aerosol optical thickness, fine mode effective radius and aerosol layer height from RSP data. Among the advantages of using a neural network as initial guess for an iterative algorithm are a decrease in processing time and an increase in the number of converging retrievals.

scholarly journals Nearly Exponential Neural Networks Approximation in Lp Spaces

2017 ◽  
Vol 26 (1) ◽  
pp. 103-113
Author(s):  
Eman Samir Bhaya ‎ ◽  
Zahraa Mahmoud Fadel
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Continuous Function ◽  
Real Function ◽  
Convex Subset ◽  
Exponential Approximation ◽  
Lp Spaces ◽  
The Neural Network ◽  
Hidden Layer ◽  
Engineering Physics

In different applications, we can widely use the neural network approximation. They are being applied to solve many problems in computer science, engineering, physics, etc. The reason for successful application of neural network approximation is the neural network ability to approximate arbitrary function. In the last 30 years, many papers have been published showing that we can approximate any continuous function defined on a compact subset of the Euclidean spaces of dimensions greater than 1, uniformly using a neural network with one hidden layer. Here we prove that any real function in L_P (C) defined on a compact and convex subset  of can be approximated by a sigmoidal neural network with one hidden layer, that we call nearly exponential approximation.

Solution of the problem of forecasting based on neural networks

2020 ◽  
pp. 45-48
Author(s):  
E.V. Kuliev ◽  
N.V. Grigorieva ◽  
M.A. Dovgalev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Life Cycle ◽  
Continuous Function ◽  
Human Brain ◽  
Arbitrary Continuous Function ◽  
The Neural Network ◽  
Nonlinear Neural Networks

This article is about prediction using neural networks. Neural networks are used to solve problems that require analytical calculations similar to those carried out by the human brain. Inherently nonlinear neural networks allow to approximate an arbitrary continuous function with any degree of accuracy, regardless of the absence or presence of any periodicity or cyclicality. Today, neural networks are one of the most powerful forecasting mechanisms. This article discusses the General principles of training and operation of the neural network, the life cycle, the solution of forecasting problems using the approximation of the function.

scholarly journals Combined neural network/Phillips–Tikhonov approach to aerosol retrievals over land from the NASA Research Scanning Polarimeter

2017 ◽  
Vol 10 (11) ◽  
pp. 4235-4252 ◽  
Author(s):  
Antonio Di Noia ◽  
Otto P. Hasekamp ◽  
Lianghai Wu ◽  
Bastiaan van Diedenhoven ◽  
Brian Cairns ◽  
...  
Keyword(s):  
Neural Network ◽  
Land Surface ◽  
Iterative Scheme ◽  
Large Data ◽  
Initial Guess ◽  
Effective Radius ◽  
Aerosol Layer ◽  
Data Set ◽  
The Neural Network ◽  
Fine Mode

Abstract. In this paper, an algorithm for the retrieval of aerosol and land surface properties from airborne spectropolarimetric measurements – combining neural networks and an iterative scheme based on Phillips–Tikhonov regularization – is described. The algorithm – which is an extension of a scheme previously designed for ground-based retrievals – is applied to measurements from the Research Scanning Polarimeter (RSP) on board the NASA ER-2 aircraft. A neural network, trained on a large data set of synthetic measurements, is applied to perform aerosol retrievals from real RSP data, and the neural network retrievals are subsequently used as a first guess for the Phillips–Tikhonov retrieval. The resulting algorithm appears capable of accurately retrieving aerosol optical thickness, fine-mode effective radius and aerosol layer height from RSP data. Among the advantages of using a neural network as initial guess for an iterative algorithm are a decrease in processing time and an increase in the number of converging retrievals.

scholarly journals Analysis for Mutual Impedance of Pistons by Neural Network and Its Extension of Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Kun-Chou Lee
Keyword(s):  
Neural Network ◽  
Mutual Coupling ◽  
Mathematical Problem ◽  
Underwater Communication ◽  
Challenging Problem ◽  
Numerical Examples ◽  
Mutual Impedance ◽  
Sonar System ◽  
The Neural Network ◽  
Network Output

This study is basically a mathematical problem in sonar engineering. The sonar plays a very important role in underwater communication, detection, and remote sensing. Pistons are key sensors in a sonar system. The mutual coupling is a challenging problem in designing a sonar array. The mutual impedance of pistons is required in analyzing the mutual coupling of a sonar array. In this paper, a mathematical model consisting of a neural network and its extension of derivative is given and then utilized to analyze the mutual impedance of pistons. Initially, the mutual impedance of pistons is modelled and predicted by a neural network. By suitably extending the neural network, the derivative, i.e., slope information, for the neural-network output is obtained easily. Therefore, the mutual impedance and its slope information are obtained simultaneously almost in real time as the neural network is well trained in advance. Numerical examples show that the neural network can accurately predict the mutual impedance and its extension of derivative gives the slope information of mutual impedance simultaneously. It should be emphasized that the training work of a neural network is performed only once, i.e., only the training work in mapping the mutual impedance is required. No additional training work is required in obtaining the slope information.

scholarly journals Inversion of HF Radar Doppler Spectra Using a Neural Network

2019 ◽  
Vol 7 (8) ◽  
pp. 255 ◽  
Author(s):  
Rachael L. Hardman ◽  
Lucy R. Wyatt
Keyword(s):  
Neural Network ◽  
Radar Data ◽  
Hf Radar ◽  
Radar Signal ◽  
Inversion Method ◽  
Wave Direction ◽  
Ocean Engineering ◽  
The Neural Network ◽  
Viable Solution ◽  
Positive Results

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.

Sign in / Sign up

Export Citation Format

Share Document