The manufacturing processes and design of metal and alloy products can be performed over a wide range of strain rates and temperatures. To design and optimize these processes using computational mechanics tools, the selection and calibration of the constitutive models is critical. In the case of hazardous and explosive impact loads, it is not always possible to test material properties. For this purpose, this paper assesses the efficiency and the accuracy of different architectures of ANNs for the identification of the Johnson-Cook material model parameters. The implemented computational tool of an ANN-based parameter identification strategy provides adequate results in a range of strain rates required for general manufacturing and product design applications. Four ANN architectures are studied to find the most suitable configuration for a reduced amount of experimental data, particularly for cases where high-impact testing is constrained. The different ANN structures are evaluated based on the model's predictive capability, revealing that the perceptron-based network of 66 inputs and one hidden layer of 30 neurons provides the highest prediction accuracy of the effective flow stress-strain behavior of Ti64 alloy and three virtual materials.