Topology-Informed Framework Designs Multicellular Patterns with ABMs

Designing and understanding complex multicellular patterns, such as those found in biological development, often relies on agent-based models (ABMs). However, a significant challenge in these models is accurately estimating the cell-level parameters that govern pattern formation, especially under stochastic conditions of cell proliferation and death. Quantitatively evaluating the topological characteristics of these arrangements is also difficult. Researchers have developed TI$^2$PS, a Topology-Informed Inverse Design Framework, to address these issues. The framework combines two key methodologies: Betti vectors derived from topological data analysis, which provide a consistent way to represent features of diverse multicellular spatial configurations, and inverse surrogate modeling, which directly infers ABM parameters from target patterns. The efficacy of TI$^2$PS was validated using zebrafish pigment pattern formation as a model system. Results showed that the framework successfully estimated ABM parameters and significantly outperformed conventional methods like PointNet++. Remarkably, TI$^2$PS achieved superior performance using only 10% of the training data that PointNet++ required, demonstrating its efficiency and robustness across all evaluation metrics.