In many regression applications, there exist common cases for users to know qualitatively, yet partially, about nonlinear relationships of physical systems. This paper presents a novel direction for constructing feedforward neural networks (FNNs) which are subject to the given nonlinear relationships. The “Integrated models”, associating FNNs with the given nonlinear functions, are proposed. Significant benefits will be obtained over the conventional FNNs by using these models. First, they add a certain degree of comprehensive power for nonlinear approximators. Second, they may provide better generalization capabilities. Two issues are discussed about the improved approximation and the estimation of the real parameters to the partially known function in the proposed models. Numerical studies are given in comparing with the conventional FNNs. This work is supported in part by National Science Foundation of China (#60275025, #60121302) and Chinese 863 Program (#2002AA241221).n many regression applications, there exist common cases for users to know qualitatively, yet partially, about nonlinear relationships of physical systems. This paper presents a novel direction for constructing feedforward neural networks (FNNs) which are subject to the given nonlinear relationships. The “Integrated models”, associating FNNs with the given nonlinear functions, are proposed. Significant benefits will be obtained over the conventional FNNs by using these models. First, they add a certain degree of comprehensive power for nonlinear approximators. Second, they may provide better generalization capabilities. Two issues are discussed about the improved approximation and the estimation of the real parameters to the partially known function in the proposed models. Numerical studies are given in comparing with the conventional FNNs. This work is supported in part by National Science Foundation of China (#60275025, #60121302) and Chinese 863 Program (#2002AA241221).