Lab-on-a-chip (LoC) systems can be functionally decomposed into their basic operating devices. Common devices are mixers, reactors, injectors, and separators. In this paper, the injector device is modeled using artificial neural networks (NNs) trained with finite element simulations of the underlying mass transport partial differential equations (PDEs). This technique is used to map the injector behavior into a set of analytical performance functions parameterized by the system's physical variables. The injector examples shown are the cross, the double-tee, and the gated-cross. The results are four orders of magnitude faster than numerical simulation and accurate with mean square errors (MSEs) on the order of$10^-4$. The resulting NN training data compare favorably with experimental data from a gated-cross injector found in the literature.