利用大语言模型进行参数化形状优化
Using Large Language Models for Parametric Shape Optimization
AI总结：
本研究提出基于大语言模型的参数化形状优化框架LLM-PSO，借鉴进化策略用Claude 3.5 Sonnet求解两类流动减阻优化问题，收敛速度优于经典算法，为工程设计优化提供新思路。
摘要：
近期先进的大语言模型（LLM）展现出涌现的上下文学习能力，无需重新训练即可通过自然语言提示实现智能决策。这种新的机器学习范式在包括通用控制与优化问题在内的多个领域展现出应用前景。受这些进展启发，我们探索了LLM在一项具体且关键的工程任务中的潜力：参数化形状优化（PSO）。我们开发了LLM-PSO优化框架，该框架借鉴进化策略的思路，利用LLM确定参数化工程设计的最优形状。我们使用Claude 3.5 Sonnet LLM，在两个基准流动优化问题上评估了LLM-PSO，具体目标是识别以下两类场景的最小阻力外形：1）层流中的二维翼型，2）斯托克斯流中的三维轴对称体。在两个案例中，LLM-PSO均成功识别出与基准解一致的最优形状，且其收敛速度通常快于其他经典优化算法。我们的初步探索可为进一步研究利用LLM开展形状优化及更广泛的工程设计提供启发。
英文摘要：
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.
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