In this paper we present Cellular Neural Networks (CNN) with a new type of nonlinear weight functions. Instead of representing a weight function by a n-th order polynom, we propose tabulated functions by using a cubic spline interpolation procedure. These CNN are considered for the problem of modelling nonlinear systems, which are characterized by partial differential equations (PDE). Therefore we propose a training algorithm to adjust the behaviour of CNN solutions to the solutions of a given nonlinear system. Results are given for the Φ⁴-equation and the achieved accuracy is compared to the approximation accuracy of solutions obtained by a direct spatial discretization of the Φ⁴-equation.