This paper presents experimental and computational findings related to the compressive strength of concrete containing nano-SiO2, fly-ash, silica fume, and polycarboxylate-superplasticizer. At different days of aging, three central-composite experimental designs were performed to assess the role of the input variables. The statistical results indicated linear, interactive, and quadratic effects between the variables as well as mathematical lack-of-fit of the second-order. Hence, artificial neural networks (ANN) with multiple inputs were implemented to assist in understanding the complex nature of the systems. The results indicated that, by using ANN, the compressive strength of the systems could be modeled to improve the concrete´s performance acting in conjunction with results obtained from the statistical experimental designs. Sensitivity analyses on the ANN-simulations allowed for quantifying the influence of the multiple input variables and results were physically related to the mathematical lack-of-fit condition inherit in the statistical experimental designs.