# Restricted gene expression programming: a new approach for parameter identification inverse problems of partial differential equation

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## Abstract

Traditionally, solving the parameter identification inverse problems of partial differential equation encountered many difficulties and insufficiency. In this article, we proposed a restricted gene expression programming (GEP) for parameter identification inverse problems of partial differential equation based on the self-adaption, self-organization, and self-learning characters of GEP. The algorithm simulates parametric function itself of partial differential equation directly through the observed values by taking effect to inverse results caused by noise of the measured value into full consideration. Modeling is unnecessary to add regularization in modeling process aiming at special problems again. The experiment results also showed that the algorithm has good noise-immunity. In case there is no noise or noise is very low, the identified parametric function is almost the same as the original accurate value; when noise is very high, accurate result can still be obtained, which successfully realizes automation of parameter modeling process for partial differential equation.

## Keywords

Gene expression programming Partial differential equation Inverse problems Thomas algorithm## Notes

### Acknowledgments

This work was supported by the National Natural Science Foundation of China with the Grant No. 61573157 and the Fund of Science and Technology Planning Project of Guangdong Province of China with the Grant No. 2015A020209108.

### Compliance with ethical standards

#### Conflict of interest

The authors declare that they have no conflict of interest.

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