Differentiable Design for Morphogenesis I: Simulation and Simulacra

Abstract

Cells build tissues through local exchanges of force and information, yet the rules governing these interactions are difficult to infer from sparse observations. Here, we introduce waxMorph, a differentiable cell-based framework for generating and reconstructing three-dimensional morphogenesis. In synthetic and biological data, waxMorph reproduced established mechanochemical shape programs, inferred continuous trajectories from static tissue volumes, and recovered spatially organized latent signals. In a developing mouse myocardium dataset, it reconstructed unobserved intermediate geometries more accurately than optimal-transport interpolation, while in forelimbs it distinguished related developmental trajectories. By varying the capacity and spatial organization of the latent cues available to cells, waxMorph also provides a model-based way to quantify the complexity of shape assembly. waxMorph is built within the spatial-computing ecosystem of NVIDIA Warp. It provides an open-source, Python-native, GPU-accelerated, hybrid physics-AI framework for learning how local cellular interactions give rise to biological form.