Constructing the reduction model of large-scale pattern dynamics is challenging. In this study, a framework is proposed to estimate a reduction model of the gradient system, often observed in various pattern dynamics, in a data-driven manner using a deep learning model inspired by Hamiltonian neural networks for video. Furthermore, the proposed framework verifies whether the reduction model is consistent with the phenomenon and contains useful properties. To demonstrate its usefulness, it is applied to the numerical calculation data of magnetic domain pattern formation. Consequently, the previous reduction model proposed for magnetic domain pattern dynamics is found to be insufficient to explain the phenomenon, and suggestions for possible directions for the improvement of the reduction model are provided.