In this paper, we introduce LInK, a novel framework that integrates contrastive learning of performance and design space with optimization techniques for solving complex inverse problems in engineering design with discrete and continuous variables. We focus on the path synthesis problem for planar linkage mechanisms. By leveraging a multimodal and transformation-invariant contrastive learning framework, LInK learns a joint representation that captures complex physics and design representations of mechanisms, enabling rapid retrieval from a vast dataset of over 10 million mechanisms. This approach improves precision through the warm start of a hierarchical unconstrained nonlinear optimization algorithm, combining the robustness of traditional optimization with the speed and adaptability of modern deep learning methods. Our results on an existing benchmark demonstrate that LInK outperforms existing methods with 28 times less error compared to a state of the art approach while taking 20 times less time on an existing benchmark. Moreover, we introduce a significantly more challenging benchmark, named LINK ABC, which involves synthesizing linkages that trace the trajectories of English capital alphabets, an inverse design benchmark task that existing methods struggle with due to large nonlinearities and tiny feasible space. Our results demonstrate that LInK not only advances the field of mechanism design but also broadens the applicability of contrastive learning and optimization to other areas of engineering. The code and data are publicly available at https://github.com/ahnobari/LInK.

翻译：本文提出LInK这一创新框架，该框架通过整合性能与设计空间的对比学习及优化技术，用于解决包含离散与连续变量的复杂工程反演问题。我们聚焦于平面连杆机构的轨迹综合问题。通过利用多模态且具有变换不变性的对比学习框架，LInK能够学习捕捉机构复杂物理特性与设计特征的联合表示，从而实现对超过1000万个机构的大规模数据集进行快速检索。该方法通过为分层无约束非线性优化算法提供热启动来提升精度，将传统优化方法的鲁棒性与现代深度学习方法的快速性和适应性相结合。在现有基准测试上的结果表明，LInK优于现有方法，与最先进方法相比误差降低28倍，同时在现有基准测试上耗时减少20倍。此外，我们提出了一个更具挑战性的新基准测试集LINK ABC，其涉及综合能描绘英文大写字母轨迹的连杆机构——这一反演设计基准任务因高度非线性及极小的可行解空间而使现有方法难以应对。我们的结果表明，LInK不仅推动了机构设计领域的发展，还将对比学习与优化方法的适用性拓展至工程的其他领域。代码与数据已公开于https://github.com/ahnobari/LInK。