用于拓扑优化的轨迹感知流匹配
Trajectory-Aware Flow Matching for Topology Optimisation
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology（昆士兰科技大学机械、医学与过程工程学院）
- Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University（清华大学工程力学系生物力学与医学工程研究所）
- School of Civil and Environmental Engineering, Queensland University of Technology（昆士兰科技大学土木与环境工程学院）
- State Key Laboratory of Advanced Environmental Technology, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences（中国科学院广州地球化学研究所环境技术重点实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究针对拓扑优化中成本高、现有模型依赖复杂方法的问题，开发基于流匹配的拓扑优化（FMTO）框架，通过轨迹感知公式将物理引导优化历史纳入生成流学习，经分析和示例验证其能提升性能，适用于二维及三维问题。
AI中文摘要：
拓扑优化（TO）通常需要重复进行有限元分析和基于灵敏度的材料更新，在不同物理和设计条件下需要多个候选设计时成本很高。生成式TO为快速设计探索提供了途径，但现有模型可能依赖对抗训练、长时间反向扩散采样或外部指导来维持结构可行性和物理一致性。本研究开发了一种基于流匹配的拓扑优化（FMTO）框架用于条件拓扑生成。首先将线性FMTO制定为基于端点的基线，通过在高斯源场和BESO参考拓扑之间进行插值。为引入有机械意义的中间状态，提出了轨迹感知FMTO公式，使用体积分数索引的BESO状态来构建概率路径和目标速度场。这将物理引导的优化历史纳入生成流学习而无需添加推理时优化。路径 - 速度失配分析解释了为何适度的轨迹加权可提高生成稳定性，而过度引导可能过度约束学习到的传输。数值示例表明，FMTO生成了具有改进的与柔顺性相关性能、体积分数满意度、拓扑保真度的多样拓扑候选，且采样步骤比基于扩散的基线少得多。在有限训练数据下，轨迹感知FMTO以适度的轨迹权重实现了最佳整体性能。对轨迹锚密度和三维拓扑生成的研究进一步证明了路径设计的影响以及所提出框架在二维问题之外的适用性。
英文摘要：
Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions. Generative TO offers a route to rapid design exploration, but existing models may rely on adversarial training, long reverse-diffusion sampling, or external guidance to maintain structural feasibility and physical consistency. This study develops a flow matching-based topology optimisation (FMTO) framework for conditional topology generation. Linear FMTO is first formulated as an endpoint-based baseline by interpolating between a Gaussian source field and the BESO reference topology. To introduce mechanically meaningful intermediate states, a trajectory-aware FMTO formulation is proposed, where volume-fraction-indexed BESO states are used to construct the probability path and target velocity field. This incorporates physics-guided optimisation history into generative flow learning without adding inference-time optimisation. A path--velocity mismatch analysis explains why moderate trajectory weighting can improve generation stability, whereas excessive guidance may over-constrain the learned transport. Numerical examples show that FMTO generates diverse topology candidates with improved compliance-related performance, volume-fraction satisfaction, topology fidelity, and substantially fewer sampling steps than a diffusion-based baseline. Under limited training data, trajectory-aware FMTO achieves the best overall performance with a moderate trajectory weight. Studies on trajectory-anchor density and three-dimensional topology generation further demonstrate the influence of path design and the applicability of the proposed framework beyond two-dimensional problems.
