Numerical methods for identifying the diffusion coefficient in a nonlinear elliptic equation

Two different approaches for solving a nonlinear coefficient inverse problem are investigated in this paper. As a classical approach, we use the finite element method to discretize the direct and inverse problems and solve the inverse problem by the conjugate gradient method. Meanwhile, we also apply the neural network approach to recover the coefficient of the inverse problem, which is to map measurements at some fixed points and the unknown coefficient. According to the results of applying the two approaches, our methods are shown to solve the nonlinear coefficient inverse problem efficiently, even with perturbed data.