This work proposes a statistical modeling approach for the artificial neural network (ANN)-based compact model (CM). The method of retaining part of the network features of the nominal device and further finetuning the network parameters (variational neurons) is found to accurately reproduce the static variation. A mapping from process variation to network parameters is derived by combining the proposed variational neuron selection algorithm and the backward propagation of variance (BPV) method. In addition, a secondary classification of the selected variational neurons is applied to model the fabrication-induced correlation between n- and p-type devices. The neural network-based statistical modeling approach has been well implemented and verified on the GAA simulation data and the 16nm node foundry FinFET, which indicates its great potential in modeling emerging and advanced device technology.