Denoising diffusion models for inverse design of inflatable structures with programmable deformations

Programmable structures are systems whose undeformed geometries and material property distributions are deliberately designed to achieve prescribed deformed configurations under specific loading conditions. Inflatable structures are a prominent example, using internal pressurization to realize large, nonlinear deformations in applications ranging from soft robotics and deployable aerospace systems to biomedical devices and adaptive architecture. We present a generative design framework based on denoising diffusion probabilistic models (DDPMs) for the inverse design of elastic structures undergoing large, nonlinear deformations under pressure-driven actuation. The method formulates the inverse design as a conditional generation task, using geometric descriptors of target deformed states as inputs and outputting image-based representations of the undeformed configuration. Representing these configurations as simple images is achieved by establishing a pre- and postprocessing pipeline that involves a fixed image processing, simulation setup, and descriptor extraction methods. Numerical experiments with scalar and higher-dimensional descriptors show that the framework can quickly produce diverse undeformed configurations that achieve the desired deformations when inflated, enabling parallel exploration of viable design candidates while accommodating complex constraints.