An Evolutionary Parameter Inversion Approach
Xiong Sheng · Wuhan University Journal · 2001
An inverse problem is to determine unknown causes based on observation of their effects. Such problems often arise in scientific research and engineering practice. We presented a general methodology based on evolutionary algorithms (EAs) for the parameter estimation of inverse problems. Giving function class of unknown parameter, genetic algorithms (GA) is used to evolve the optimal coefficient of linear combination of basis function. Without giving the class of parameter function, genetic programming (GP) is used to evolve the appropriate parameter function structure and coefficient such that the identification of parameter is objective and automatically. When applying ordinary differential equations (ODEs) or partial differential equations (PDEs) including unknown parameter to prediction models, the parameter is adaptively calibrated according to the recent observation data such that the prediction is improved by evolutionary computation. We apply this method to the numerical recovery of spatially varying physical parameters in elliptic boundary values problems. The successful numerical results demonstrated that the proposed method has the potential to solve a wide range of inverse parameter identification problems in a systematic and robust way.