# Self-Refining Topology Optimization via an LLM-Based Multi-Agent Framework

arXiv: https://arxiv.org/abs/2605.23273 · HTML: https://mlsanity.com/paper/2605.23273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal and embodied agents, one of 16 directions in LLM agents and tool use.
- Builds on 18 of its 58 references that are in the map.
- First posted on arXiv 22 May 2026.

## Placed in

- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)

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

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- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
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- [CodeCoR: An LLM-Based Self-Reflective Multi-Agent Framework for Code Generation](https://mlsanity.com/paper/2501.07811/) (2025)
- [Multi-Agent-as-Judge: Aligning LLM-Agent-Based Automated Evaluation with Multi-Dimensional Human Evaluation](https://mlsanity.com/paper/2507.21028/) (2025)
- [MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problems](https://mlsanity.com/paper/2306.17525/) (2023)
- [Large Language Model Agent as a Mechanical Designer](https://mlsanity.com/paper/2404.17525/) (2024)
- [OmniScience: A Domain-Specialized LLM for Scientific Reasoning and Discovery](https://mlsanity.com/paper/2503.17604/) (2025)
- [ALL-FEM: Agentic Large Language models Fine-tuned for Finite Element Methods](https://mlsanity.com/paper/2603.21011/) (2026)
- [GraphAgents: Knowledge Graph-Guided Agentic AI for Cross-Domain Materials Design](https://mlsanity.com/paper/2602.07491/) (2026)

## Abstract (arXiv)

Topology optimization is a widely used design method that produces optimized material distributions for prescribed objectives and constraints through well-established numerical algorithms. Throughout the workflow, engineers make a series of decisions ranging from setting and adjusting numerical parameters to assessing whether the converged design meets considerations beyond those explicitly included in the optimization problem, such as physical feasibility. These decisions, which draw on domain expertise, interfere with the autonomous design process. To address this difficulty, this study presents TopOptAgents, a multi-agent system for automating not only the design process but also decision-making during the key stages of the topology optimization process. TopOptAgents consists of six LLM-based agents collaborating through iterative self-refinement cycles spanning problem formulation, validation, code generation and execution, and quality assessment of the optimized structure. This process enables error correction and progressive improvement of both the optimization setup and resulting design. The framework is demonstrated on optimization problems selected to cover a range of settings that differ in their literature coverage and numerical characteristics The benefits of iterative self-refinement are found to be particularly pronounced for problem classes where the pretrained language model has limited prior exposure, such as formulations whose literature and open-source implementations are comparatively sparse. In such cases, the proposed framework reliably produces converged designs where a single state-of-the-art LLM struggles, suggesting that self-refinement broadens the range of topology optimization problems that LLM-based automation can reliably address.