# Using Large Language Models for Parametric Shape Optimization

arXiv: https://arxiv.org/abs/2412.08072 · HTML: https://mlsanity.com/paper/2412.08072/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 74 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Builds on (most cited first, 18 of 18)

- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Shap-E: Generating Conditional 3D Implicit Functions](https://mlsanity.com/paper/2305.02463/) (2023)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [Prompt a Robot to Walk with Large Language Models](https://mlsanity.com/paper/2309.09969/) (2023)
- [MetaOpenFOAM: an LLM-based multi-agent framework for CFD](https://mlsanity.com/paper/2407.21320/) (2024)
- [Towards Optimizing with Large Language Models](https://mlsanity.com/paper/2310.05204/) (2023)
- [Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism](https://mlsanity.com/paper/2403.02054/) (2024)
- [Pre-Trained Large Language Models for Industrial Control](https://mlsanity.com/paper/2308.03028/) (2023)
- [MyCrunchGPT: A chatGPT assisted framework for scientific machine learning](https://mlsanity.com/paper/2306.15551/) (2023)
- [FLUID-LLM: Learning Computational Fluid Dynamics with Spatiotemporal-aware Large Language Models](https://mlsanity.com/paper/2406.04501/) (2024)
- [Generative VS non-Generative Models in Engineering Shape Optimization](https://mlsanity.com/paper/2402.08540/) (2024)
- [Training microrobots to swim by a large language model](https://mlsanity.com/paper/2402.00044/) (2024)

## Built on by (most cited first, 7 of 7)

- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [Generative Reliability-Based Design Optimization Using In-Context Learning Capabilities of Large Language Models](https://mlsanity.com/paper/2503.22401/) (2025)
- [Engineering.ai: A Platform for Teams of AI Engineers in Computational Design](https://mlsanity.com/paper/2511.00122/) (2025)
- [TurboAgent: An LLM-Driven Autonomous Multi-Agent Framework for Turbomachinery Aerodynamic Design](https://mlsanity.com/paper/2604.06747/) (2026)
- [LinguaFluid: Language Guided Fluid Control via Semantic Rewards in Reinforcement Learning](https://mlsanity.com/paper/2508.05977/) (2025)
- [AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control](https://mlsanity.com/paper/2603.27000/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)

## Abstract (arXiv)

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.