Trainable Multicellular Phase-Field Model for Targeted Pattern Formation via Local Interactions

Multicellular systems form diverse morphologies through chemical and physical interactions among cells. In this study, we propose a trainable multicellular phase-field model that incorporates a neural network. The phase-field model represents cell morphology and position as continuous fields and serves as the basis for learning intercellular dynamics. In the proposed model, the neural network takes the local state as input and predicts the subsequent state, adjusting the spatial evolution of the multicellular system to approach a target pattern defined by a loss function. Through simulation experiments, we confirmed that the trained neural network enables cells to aggregate into a cluster and reproduce the spatial pattern of a given image. Moreover, similar results were obtained in a larger simulation domain than that used during training, demonstrating the scalability of the model.