Recent advanced large language models (LLMs) have showcased their emergent capability of in-context learning, facilitating intelligent decision-making through natural language prompts without retraining. This new machine learning paradigm has shown promise in various fields, including general control and optimization problems. Inspired by these advancements, we explore the potential of LLMs for a specific and essential engineering task: parametric shape optimization (PSO). We develop an optimization framework, LLM-PSO, that leverages an LLM to determine the optimal shape of parameterized engineering designs in the spirit of evolutionary strategies. Utilizing the ``Claude 3.5 Sonnet'' LLM, we evaluate LLM-PSO on two benchmark flow optimization problems, specifically aiming to identify drag-minimizing profiles for 1) a two-dimensional airfoil in laminar flow, and 2) a three-dimensional axisymmetric body in Stokes flow. In both cases, LLM-PSO successfully identifies optimal shapes in agreement with benchmark solutions. Besides, it generally converges faster than other classical optimization algorithms. Our preliminary exploration may inspire further investigations into harnessing LLMs for shape optimization and engineering design more broadly.

翻译：近期先进的大型语言模型（LLMs）展现了其新兴的上下文学习能力，能够通过自然语言提示实现智能决策而无需重新训练。这种新的机器学习范式已在包括通用控制与优化问题在内的多个领域展现出潜力。受这些进展的启发，我们探索了LLMs在特定且重要的工程任务——参数化形状优化（PSO）中的应用潜力。我们开发了一个优化框架LLM-PSO，该框架借鉴进化策略的思想，利用LLM来确定参数化工程设计的最优形状。通过使用"Claude 3.5 Sonnet" LLM，我们在两个基准流动优化问题上评估了LLM-PSO的性能，具体目标为：1）层流中的二维翼型，2）斯托克斯流中的三维轴对称体，识别其减阻最优轮廓。在两种情况下，LLM-PSO均成功识别出与基准解一致的最优形状。此外，其收敛速度通常快于其他经典优化算法。我们的初步探索有望进一步推动利用LLMs进行形状优化及更广泛工程设计的研究。