Behaviour-oriented diffusion models, available in literature, reasonably describe the time evolution of the cross-shore position of coastal profiles (depth as a function of the distance to shore line). In previous works, we were able to identify the time-independent, but space-dependent coefficients, in 1D (and later in 2D) behaviour-oriented diffusion models for the time dynamics of long-term coastal profile evolution. Models with such coefficients even predict the depth profile evolution for some years ahead. We now focus on the structure of the so-called Cost Functional (CF), which is used to identify the coefficients above. An optimized version of CF provides smaller relative error predicting the depth profile evolution.