Artificial neural network approximations of Cauchy inverse problem for linear PDEs

Abstract In order to obtain reliable results of computations in civil engineering, the numerical procedures that are used at the stage of design should be calibrated by comparison of the theoretical results with an observed behavior of previously modeled and then executed structures. The hybrid Finite Element code with an Artificial Neural Network inserted as a representation of a constitutive law, offers a possibility to adjust not only parameters of the constitutive relationships but also its qualitative form. Because of this, the representation of constitutive law by the ANN is presented in this paper. The constitutive data should be calibrated to fit well the observable values, measured in experiments. If the constitutive law is expressed by ANN, the inverse problem can be reduce to a training of the ANN inserted into the Finite Element code. An example of a solution of the inverse problem in calibration of constitutive law is presented. An identification of parameters of flow of pollutant in soils is described as another example of application of ANN in engineering

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Inverse Problem with Respect to Domain and Artificial Neural Network Algorithm for the Solution

Mathematical Problems in Engineering ◽

10.1155/2011/145608 ◽

2011 ◽

Vol 2011 ◽

pp. 1-16 ◽

Cited By ~ 2

Author(s):

Kambiz Majidzadeh

Keyword(s):

Neural Network ◽

Inverse Problem ◽

Artificial Neural Network ◽

Solution Algorithm ◽

Effective Solution ◽

Equivalent Problem ◽

New Approach ◽

Neural Network Algorithm ◽

Artificial Neural ◽

Artificial Neural Network Algorithm

We consider the inverse problem with respect to domain. We suggested a new approach for reducing the inverse problem for a domain to an equivalent problem in a variational setting and gave an effective solution algorithm for solving such problems. In order to solve boundary problem, the artificial neural network is used in each step of the iteration.

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An Artificial Neural Network Model to Predict Material Characteristics From the Results of Miniature Disk Bending Tests

Journal of Pressure Vessel Technology ◽

10.1115/1.4027320 ◽

2014 ◽

Vol 137 (1) ◽

Author(s):

A. K. Ghosh ◽

Vishnu Verma ◽

G. Behera

Keyword(s):

Neural Network ◽

Mechanical Properties ◽

Inverse Problem ◽

Artificial Neural Network ◽

Material Properties ◽

Artificial Neural Network Model ◽

Large Database ◽

Bending Tests ◽

Artificial Neural ◽

Artificial Neural Network Ann

The inverse problem of evaluating mechanical properties of material from the observed values of load and deflection of a miniature disk bending specimen is discussed in this paper. It involves analysis of large amplitude, elasto-plastic deformation considering contact and friction. The approach in this work is to first generate—by a finite element (FE) solution—a large database of load-displacement (P-w) records for varying material properties. An artificial neural network (ANN) is trained with some of these data. The errors in the various values of the parameters during testing with additional known data were found to be reasonably small.

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