Large language models as optimization controllers: Adaptive continuation for SIMP topology optimization

We present a framework in which a large language model (LLM) acts as a state-conditioned software control layer for solid isotropic material with penalization (SIMP) topology optimization, selecting continuation parameters from the current solver state rather than a fixed open-loop schedule. Every k th iteration, the LLM selects p , β , r min , and δ from a structured solver-state observation through a Direct Numeric Control interface. A hard grayness gate reduces premature projection sharpening. The study compares this controller with fixed no-continuation, standard three-field continuation, an expert heuristic, and a schedule-only ablation on three 2-D benchmark types and two supporting 3-D cases from the same single-load compliance-minimization family. Additional ablation, gate, budget, replay, and model-sensitivity checks clarify attribution and reproducibility. In these single-run 2-D comparisons, the LLM controller reduces final compliance by 5.9%–7.4% relative to the no-tail fixed baseline and is better than the expert, three-field, schedule-only, and grayness-rule controllers. A strong fixed+tail control is slightly better (0.4%–1.1%) than the tuned LLM on the same standardized 2-D cases, so late-stage sharpening itself accounts for an important portion of the improvement over the no-tail baseline. The LLM contribution is therefore a control layer that can execute and help discover competitive continuation strategies, not superior numerical performance on these 2-D cases. The reported differences are case-specific controlled comparisons within the tested benchmark family.