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基于扩散模型的拓扑优化研究
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Abstract:
拓扑优化是工业设计领域中常见的数学方法，旨在给定的物理领域内，满足各种约束条件、负载和其他边界条件等前提下，生成最佳的拓扑结构。传统的拓扑优化大多都依赖有限元方法(FEM)，然而有限元方法的迭代计算很大程度上增加了拓扑优化的时间成本和算力成本。如今，机器学习和深度学习在图像生成领域内的快速发展为拓扑优化的发展带来了机遇。扩散模型是一种无监督图像生成模型，因生成效果优秀、细节完美等特点等得到广泛使用。本文将在扩散模型的基础上提出新的网络结构，让其适应拓扑优化生成特性，根据特定信息生成与之对应的最优拓扑优化结果。
Topology optimization is a common mathematical method in the field of industrial design, aiming to generate the best topology structure in a physical field under various constraints, loads, and boundary conditions. Most of the traditional topology optimization methods are based on finite element method (FEM) the iterative calculation of which increases the time cost and the demand of computing power greatly. Nowadays, the rapid developments of machine learning and deep learning in the field of image generation have brought opportunities to improve topology optimization methods. Diffusion model is a kind of unsupervised image generation model. Since the model can generate images with more detail efficiently, it is widely used in different fields. In this paper, a novel model is proposed based on the diffusion model for topology optimization. Given the characteristic of topology optimization, this model can generate optimal topology structures according to their specific information.
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