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Crowd counting and density estimation are the principal objectives of crowd analysis, which offer significant applications in surveillance, event management, and traffic design. In the field of crowd flow, including simulations, the dynamics of crowd movement exhibit characteristics such as followability and, thus, are categorized under a distinct flow paradigm. The recent advancements in deep learning have propelled the usage of neural networks tailored for crowd counting and density estimation from video feeds. Nonetheless, prior models did not consider crowd dynamics. This study proposes a novel method that combines neural networks with crowd dynamics. Specifically, we introduced a new penalty term that represents prior knowledge of crowd dynamics and refined the neural network outputs via static/dynamic floor field models, and grid-based crowd dynamics models. Empirical evaluation on benchmark datasets demonstrated the superiority of the proposed method over existing state-of-the-art techniques. Further analysis of each scene confirmed that the crowd counting performance is highly dependent on the scene, and the impact of the three methodological components (i.e., the penalty term and the two-floor fields) on performance varies across scenes. In particular, the floor-field model tended to be more effective when there were no significant changes in the scene. Our code is available on GitHub. https://github.com/hanebarla/ FF-guided-NeuralCC