Training Stress Patterns in 3D Cellular Packings

Cells and tissues adapt to mechanical stimuli through feedback mechanisms to reorganize their internal stresses. Inspired by this biological adaptability, we investigate the possibility of training cell-level stress patterns in cellular packings with rearrangements. Specifically, we develop a contrastive learning algorithm for the 3D vertex model, in which iterative updates to the preferred shape indices (s₀) of hidden (non-target) cells are applied to achieve a prescribed maximum shear stress on target cells with high precision.

We show that the algorithm reliably trains a single target cell to reach large deviations from its initial stress state. During successful training, the distribution of hidden-cell shape parameters drifts coherently, solidifying for high target stresses and fluidizing for low ones. This reveals a compatibility constraint: multi-cell targets must converge toward a common stress level. Under this constraint, multi-cell stress patterns are also trainable; however, the number of target cells that can be trained is limited by the number of hidden cells, defining a mechanical capacity for stress learning. Finally, we demonstrate multi-pattern adaptability, in which alternating between two target patterns progressively reduces the switching cost.

Introducing such physical learning algorithms into tissue models may provide a framework for understanding how tumor spheroids and other active collectives program cell-level stresses to drive invasion or morphogenesis.