Simultaneous estimation of nonlinear parameters in parabolic partial differential equation using quantum-behaved particle swarm optimization with Gaussian mutation

Abstract

In this paper, an improved quantum-behaved particle swarm optimization with Gaussian mutation is proposed to simultaneously estimate nonlinear parameters in a one-dimensional parabolic partial differential equation (PDE). No a priori information about the functional form is available, therefore the problems may be treated as function estimation which is difficult to estimate using traditional gradient-based methods. Measurements on the boundary are used in the least square modelling. Tikhonov regularization technique is used to stabilize the ill-posed problem. The numerical benchmark and experiment results demonstrate the validity and efficiency of the proposed method to solve inverse problems of estimating nonlinear parameters in parabolic PDEs.