Over the last two decades, robust design (RD) has emerged as one of the best quality improvement tools in industry. Each step in the RD procedure plays an important role in acquiring the optimal combinations of control factors that minimize the bias and variability of a product/process. However, the premise of traditional optimization problems is based on the assumption that the relationships among the products/processes that reflect the estimated functions of input-output factors are well known. A number of recent studies have used neural networks (NNs) to discover such relationships without making any assumptions. The first purpose of this paper is to propose a new RD modeling approach that uses the optimal architecture of NN based on data obtained from the design of experiment (DoE) step of the RD process and the Akaike information criterion (AIC). The second purpose is to propose a principle of desirability functions (Dfs) for the feedback network in the NN structure. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed modeling method with both feedforward and feedback network structures in comparison to the least squares method (LSM) and the inverse problem-based (IP) response surface methodology (RSM). The results demonstrate the potential of the application of NNs to RD modeling.