用大模型动态调控拓扑优化，比传统方法更优且全二值化。
Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization
- 大模型根据实时状态动态调整优化参数，取代固定调度。
- 在多个2D/3D问题上，合规性降低5.7%至18.1%，均获全二值解。
- 适合做结构优化的科研与工程人员，尤其关注自适应控制者。
本文提出一种框架，让大语言模型（LLM）作为SIMP拓扑优化的在线自适应控制器，以实时状态驱动的参数决策替代传统固定时序的延续策略。每第 $k$ 步迭代，LLM接收包含当前合规性、灰度指数、停滞计数器、棋盘效应度量、体积分数和预算消耗的结构化观测，并通过直接数值控制接口输出惩罚指数 $p$、投影锐度 $β$、滤波半径 $r_{ ext{min}}$ 与移动极限 $δ$。硬灰度门防止过早二值化，元优化循环则使用第二个LLM调优代理的调用频率与门限阈值。在三个2D问题（悬臂梁、MBB梁、L型板）和两个3D问题（悬臂梁、MBB梁）上进行测试，分辨率分别为 $120\times60$ 与 $40\times20\times10$，所有实验运行300次迭代。采用标准化的40步锐化尾部处理，使合规性差异仅反映探索阶段表现。结果显示，该代理在所有基准上均取得最低最终合规性，相较固定基线下降5.7%至18.1%，且所有解均为完全二值。仅调度的消融实验在其中两个问题上表现低于固定基线，证实性能提升源于实时干预而非调度几何设计。代码与复现脚本将在发表后公开。
原文摘要 · Abstract (English)
We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time, state-conditioned parameter decisions. At every $k$-th iteration, the LLM receives a structured observation$-$current compliance, grayness index, stagnation counter, checkerboard measure, volume fraction, and budget consumption$-$and outputs numerical values for the penalization exponent $p$, projection sharpness $β$, filter radius $r_{\min}$, and move limit $δ$ via a Direct Numeric Control interface. A hard grayness gate prevents premature binarization, and a meta-optimization loop uses a second LLM pass to tune the agent's call frequency and gate threshold across runs. We benchmark the agent against four baselines$-$fixed (no-continuation), standard three-field continuation, an expert heuristic, and a schedule-only ablation$-$on three 2-D problems (cantilever, MBB beam, L-bracket) at $120\!\times\!60$ resolution and two 3-D problems (cantilever, MBB beam) at $40\!\times\!20\!\times\!10$ resolution, all run for 300 iterations. A standardized 40-iteration sharpening tail is applied from the best valid snapshot so that compliance differences reflect only the exploration phase. The LLM agent achieves the lowest final compliance on every benchmark: $-5.7\%$ to $-18.1\%$ relative to the fixed baseline, with all solutions fully binary. The schedule-only ablation underperforms the fixed baseline on two of three problems, confirming that the LLM's real-time intervention$-$not the schedule geometry$-$drives the gain. Code and reproduction scripts will be released upon publication.
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