LInK: Learning Joint Representations of Design and Performance Spaces through Contrastive Learning for Mechanism Synthesis

TL;DR

LInK tackles inverse design of planar linkages, a mixed combinatorial-continuous problem, by learning a joint embedding of design (graph-based) and performance (kinematics) spaces through cross-modal contrastive learning and a GPU-accelerated, hierarchical optimization pipeline. The approach introduces the Graph Isomorphism Hop-Attention (GHop) architecture for mechanism encoding, models partial target curves, and employs dual CL losses to fuse design and performance representations, enabling rapid retrieval from a dataset of over $10^7$ mechanisms and fast refinement via batch BFGS on GPUs. A MILP-based manufacturability check ensures produced designs are practically realizable, and a new LINK ABC benchmark demonstrates resilience to highly nonlinear, large-feasible-space problems. Empirically, LInK achieves about 28x lower error and 20x faster performance on established benchmarks, scales to up to 20 joints with 2000 timesteps, and demonstrates strong generalization and potential applicability to broader engineering design problems beyond linkage synthesis.

Abstract

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.

Figures (25)

• Figure 1: This figure illustrates the LInK algorithm's workflow. LInK first precomputes joint embeddings for mechanisms and curves, allowing it to retrieve numerous candidate mechanisms for any new target curve within seconds. With these high-quality initial candidates, a rapid BFGS optimization process efficiently converges to path synthesis solutions. These solutions significantly outperform existing methods in both speed and performance.
• Figure 2: This figure demonstrates the path synthesis problem which involves mixed combinatorial and continuous values. This figure also shows how mechanisms are represented as graphs.
• Figure 3: This figure shows the mechanism that traces B and the feasible region highlighted in blue, where the highlighted joint can move without causing a singularity. This shows the nonlinear and discontinuous nature of the problem and highlights the challenge of performing kinematic synthesis. This is only assuming all other joints keep the same positions. Changing the position of any joint could change the feasible region for all other joints making the problem very challenging from the perspective of conventional optimization.
• Figure 4: Overview of the cross-modal contrastive learning approach in LInK. Three different representations across multiple modalities are brought into the same embedding space using contrastive learning. The bottom figure also demonstrates the GHop architecture for hop attention that enables us to capture the kinematics of mechanisms.
• Figure 5: This figure illustrates the path the solver takes to solve the kinematics of a given mechanism, showing how the skeleton of a mechanism (combinatorial design variables) is involved in the mechanism solution. Initially, the solver starts with the known joints (i.e., fixed and actuated joints highlighted red), and step by step the solver solves joints with two solved neighbors (Eqn. \ref{['eqn:triangle']}).In this example, joint 3 (the last joint to be solved) is solved in three steps. The numbered joints indicate the order of solution.