Using large language models for parametric shape optimization

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 Claude 3.5 Sonnet as the default LLM, we evaluate LLM-PSO on three flow-involved PSO problems: (1) lift-to-drag maximization of a two-dimensional airfoil in laminar flow, (2) drag minimization of a three-dimensional axisymmetric body in Stokes flow, and (3) thermal resistance minimization of a heat exchanger's fin profile in a conjugate thermal-hydraulic setting. Across all cases, LLM-PSO reliably recovers the reference solutions while converging rapidly, matching—and occasionally surpassing—the performance of conventional optimizers. Experiments with three additional LLMs exhibit similarly robust behaviors, with newer models exhibiting better performance. Our preliminary exploration may inspire further investigations into harnessing LLMs for shape optimization and engineering design more broadly.