Equations of state (EOS) correlate thermodynamic properties and are essential for flash calculations. However, solving for an EOS can be time-consuming, and EOS do not precisely represent physical reality, causing the deviation of flash results from phase equilibrium data. We propose a neural network-based EOS (NNEoS) inherently satisfying thermodynamic consistency. NNEoS first predicts the residual Gibbs energy and then derives other thermodynamic properties through differentiation. NNEoS can be trained using an analytical EOS and serve as a reliable, computationally efficient substitute. NNEoS can also be fine-tuned with experimental data to better match flash results with experimental data. We systematically evaluate the performance of NNEoS against analytical EOS on three case studies, including binary and multicomponent mixtures with and without cross-association. The results show that NNEoS achieves significantly faster flash calculations via GPU-based parallel computing and offers superior predictive accuracy after fine-tuning compared to analytical EOS.