Inverse Design for Muscle-Epithelial Bilayer Morphing System

Lizard lungs develop from a smooth epithelial surface to a corrugated 3D shape due to contractions of muscle cells. This process can be mimicked by printing an optogenetically modified muscles onto a passive epithelial layer. When stimulated by laser, the muscles contract and deform the bilayer into a 3D shape. Our research addresses the inverse problem: given a target 3D shape, what is the optimal 2D pattern of muscles? While Finite Element Analysis (FEM) can capture this deformation, two challenges arise: 1. Long simulation times make in-loop optimization infeasible, and 2. FEM is inherently non-differentiable. To address this, we discretize the system’s energy and minimize it using JAX, an auto-differentiable and GPU-accelerated package. The main challenge for the inverse problem is that the optimization can get trapped in local minima. We train a generative diffusion model to overcome this, using training data from forward simulations with different muscle patterns. The diffusion model guides reverse sampling with gradients, producing near-optimal candidates, which we refine via direct optimization. This framework offers a new approach to inverse optimization for physical systems, with applications in designing artificial organoids that mimic biological morphogenesis.