Recently CNN with nonlinear weight functions are used for various problems. Thereby nonlinear weights are represented by polynomials or tabulated functions combined with a cubic spline interpolation. In this paper a linear interpolation technique is considered to allow an accurate approximation of nonlinear weight functions in CNN. In a previous publication the Table Minimising Algorithm (TMA) was introduced and applied to the Korteweg-de Vries-equation (KdV). In this contribution new results obtained by applying the algorithm to additional partial differential equations (PDE) will be given and discussed.