Parameter Identification Inverse Problems of Partial Differential Equations Based on the Improved Gene Expression Programming

摘要

Traditionally, solving the parameter identification inverse problems of partial differential equations encountered many difficulties and insufficiency. In this paper, we propose an improved GEP (Gene Expression Programming) to identify the parameters in the reverse problems of partial differential equations based on the self-adaption, self-organization and self-learning characters of GEP. This algorithm simulates a parametric function itself of a partial differential equation directly through the observed values by fully taking into account inverse results caused by noises of a measured value. Modeling is unnecessary to add regularization in the modeling process aiming at special problems again. The experiment results show 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, good results can still be obtained, which successfully realizes automation of the parameter modeling process for partial differential equations.