Generative AIBIM, a successful structural design pipeline, has proven its ability to intelligently generate high-quality, diverse, and creative shear wall designs that are tailored to specific physical conditions. However, the current module of Generative AIBIM that generates designs, known as the physics-based conditional diffusion model (PCDM), necessitates 1000 iterations for each generation due to its reliance on the denoising diffusion probabilistic model (DDPM) sampling process. This leads to a time-consuming and computationally demanding generation process. To address this issue, this study introduces the denoising diffusion implicit model (DDIM), an accelerated generation method that replaces the DDPM sampling process in PCDM. While the original DDIM was designed for DDPM and the optimization process of PCDM differs from that of DDPM, this paper designs "DDIM sampling for PCDM," which modifies the original DDIM formulations to adapt to the optimization process of PCDM. Experimental results demonstrate that DDIM sampling for PCDM can accelerate the generation process of the original PCDM by a factor of 100 while maintaining the same visual quality in the generated results. This study effectively showcases the effectiveness of DDIM sampling for PCDM in expediting intelligent structural design. Furthermore, this paper reorganizes the contents of DDIM, focusing on the practical usage of DDIM. This change is particularly meaningful for researchers who may not possess a strong background in machine learning theory but are interested in utilizing the tool effectively.

Intelligent structural design using AI can effectively reduce time overhead and increase efficiency. It has potential to become the new design paradigm in the future to assist and even replace engineers, and so it has become a research hotspot in the academic community. However, current methods have some limitations to be addressed, whether in terms of application scope, visual quality of generated results, or evaluation metrics of results. This study proposes a comprehensive solution. Firstly, we introduce building information modeling (BIM) into intelligent structural design and establishes a structural design pipeline integrating BIM and generative AI, which is a powerful supplement to the previous frameworks that only considered CAD drawings. In order to improve the perceptual quality and details of generations, this study makes 3 contributions. Firstly, in terms of generation framework, inspired by the process of human drawing, a novel 2-stage generation framework is proposed to replace the traditional end-to-end framework to reduce the generation difficulty for AI models. Secondly, in terms of generative AI tools adopted, diffusion models (DMs) are introduced to replace widely used generative adversarial network (GAN)-based models, and a novel physics-based conditional diffusion model (PCDM) is proposed to consider different design prerequisites. Thirdly, in terms of neural networks, an attention block (AB) consisting of a self-attention block (SAB) and a parallel cross-attention block (PCAB) is designed to facilitate cross-domain data fusion. The quantitative and qualitative results demonstrate the powerful generation and representation capabilities of PCDM. Necessary ablation studies are conducted to examine the validity of the methods. This study also shows that DMs have the potential to replace GANs and become the new benchmark for generative problems in civil engineering.

In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and the Parallel Coordinate Descent Method (PCDM) of Richt\'arik and Tak\'a\v{c}. We show that the two methods are equivalent for feasibility problems up to the selection of a single step-size parameter. Furthermore, we prove an improved complexity bound for PCDM under strong convexity, and show that this bound is at least $8(L'/\bar{L})(\omega-1)^2$ times better than the best known bound for DQAM, where $\omega$ is the degree of partial separability and $L'$ and $\bar{L}$ are the maximum and average of the block Lipschitz constants of the gradient of the quadratic penalty appearing in the augmented Lagrangian.