We consider a tumor growth model initially proposed by Ward and King in 1997. Our primary goal is to find an efficient and accurate numerical method for the identification of parameters in the model (an inverse problem) from measurements of the evolving tumor over time. The so-called direct problem, in this case, is to solve a system of coupled nonlinear partial differential equations for given fixed values of the unknown parameters. We compare several derivative-free and gradient-based methods for the solution of the inverse problem which is formulated as an optimization problem with the system of partial differential equations (PDEs) as the constraint. We modify the original model by incorporating uncertainty in one of the parameters. We use the Monte Carlo method based sampling strategy, coupled with optimization methods, for the uncertainty quantification
