Generative Design of Funicular Shells via Physics-Guided Diffusion: A Hybrid PI-DDPM Architecture
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The conceptual design of funicular shells requires finding a delicate equilibrium between geometric aesthetics and strict mechanical efficiency. While numerical methods like Finite Element Analysis (FEM) are robust, their high computational cost often hinders the efficient exploration of vast design spaces. In this context, Generative Deep Learning has emerged as a powerful tool to accelerate and streamline this process. Pioneering works based on Generative Adversarial Networks (GANs) have successfully demonstrated the potential of data-driven design in this field. Building upon this success, we propose exploring Denoising Diffusion Probabilistic Models (DDPMs) as a promising complementary architecture, investigating their capabilities to generate diverse and high-fidelity structural forms. In this work, we present a novel framework specifically adapted for structural engineering that explicitly decouples the geometric generation from the physical constraints. We introduce a hybrid architecture composed of two cooperating agents: a standard DDPM that learns the distribution of valid geometries, and a noise-conditional PB-UNet that acts as a differentiable physics guide. By modeling the generation as a Langevin dynamics process, we can explicitly perturb the reverse diffusion trajectory using the gradient of a physical cost function. This allows for controllable inference where the trade-off between aesthetic diversity and structural performance can be adjusted via a guidance scale ξ, without retraining the model. This approach aims to provide a robust tool for civil engineering workflows, ensuring that the generated structures are not only visually plausible but physically consistent.