AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control

Shaoliang Yang; Jun Wang; Yunsheng Wang

cs.CEMar 27, 2026

AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control

Authors: Shaoliang Yang, Jun Wang, Yunsheng Wang

Organizations: Santa Clara University, Santa Clara, CA

Abstract

We present AutoSiMP, an autonomous pipeline that transforms a natural-language structural problem description into a validated, binary topology without manual configuration. The pipeline comprises five modules: (1) an LLM-based configurator that parses a plain-English prompt into a validated specification of geometry, supports, loads, passive regions, and mesh parameters; (2) a boundary-condition generator producing solver-ready DOF arrays, force vectors, and passive-element masks; (3) a three-field SIMP solver with Heaviside projection and pluggable continuation control; (4) an eight-check structural evaluator (connectivity, compliance, grayness, volume fraction, convergence, plus three informational quality metrics); and (5) a closed-loop retry mechanism. We evaluate on three axes. Configuration accuracy: across 10 diverse problems the configurator produces valid specifications on all cases with a median compliance penalty of $+0.3\%$ versus expert ground truth. Controller comparison: on 17 benchmarks with six controllers sharing an identical sharpening tail, the LLM controller achieves the lowest median compliance but $76.5\%$ pass rate, while the deterministic schedule achieves $100\%$ pass rate at only $+1.5\%$ higher compliance. End-to-end reliability: with the schedule controller, all LLM-configured problems pass every quality check on the first attempt $-$ no retries needed. Among the systems surveyed in this work (Table 1), AutoSiMP is the first to close the full loop from natural-language problem description to validated structural topology. The complete codebase, all specifications, and an interactive web demo will be released upon journal acceptance.

Figures & tables

System	NL input	BC gen.	TO solver	Quality eval.	Retry	Interactive UI
LLM-Struct. [ 35 ]	✓	✓	—	—	—	—
FeaGPT [ 55 ]	✓	✓	—	$\circ$	—	—
LLM-FEA [ 56 ]	✓	$\circ$	—	—	—	—
MCP-SIM [ 57 ]	✓	✓	—	✓	✓	—
LMTO [ 34 ]	✓	—	$\circ$	—	—	—
LLM-PSO [ 33 ]	—	—	—	—	—	—

Table 1: Comparison of LLM-driven engineering simulation systems. ✓= supported,

\circ

= partial, — = not supported.

Figure 1: AutoSiMP end-to-end autonomous pipeline. A natural-language prompt enters the LLM configurator (Module 1), which produces a validated ProblemSpec. The BC generator (Module 2) converts this into solver-ready arrays. The SIMP solver (Module 3) runs with a pluggable controller. The evaluator (Module 4) checks eight quality metrics. On failure, the retry loop (Module 5) adjusts parameters and re-solves (max 2 retries). The solver is consistent with Yang et al. [20] .

Figure 2: LLM Configurator detail (Module 1). A natural-language prompt (left) is processed by Gemini Flash Lite with structured JSON output mode and domain-knowledge interpretation rules (centre). The output is a validated ProblemSpec JSON (right) specifying geometry, mesh, supports, loads, and volume fraction. Deterministic safety rails clamp ranges, detect missing constraints, and validate physical consistency before the specification reaches the solver.

#	Check	Criterion	Type
1	Connectivity	Flood fill from supports to loads $\geq 0.99$	Gate
2	Compliance ratio	$C_{\text{final}}/C_{\text{best}}<2.0$	Gate
3	Grayness	$\mathcal{G}=4\,\overline{\rho(1-\rho)}\leq 0.15$	Gate
4	Volume fraction	$\|V_{f,\text{actual}}-V_{f}\|\leq 0.02$	Gate
5	Convergence	Stability or early exit	Gate
6	Thin members	Fraction of 1-element-wide connections	Metric

Table 2: Eight structural quality checks. Gates 1–5 determine pass/fail; metrics 6–8 are informational.

Figure 3: Structural quality evaluator (Module 4). The first five checks are pass/fail gates — any failure triggers a retry with adjusted parameters. Checks 6–8 are informational quality metrics reported for analysis but do not block the pipeline. Core gates (blue) ensure structural validity; informational metrics (grey) characterise design quality.

Panel of Figure 4 — Figure 4: Interactive web demo for AutoSiMP. The interface implements the complete five-module pipeline in a browser, supporting both client-side JavaScript solving (instant 2-D) and Python backend solving (production-quality 2-D/3-D with three-field SIMP and 40-iteration sharpening tail). No installation is required beyond a web browser; the Python backend is optional and consists of a single Flask file. None of the systems in Table 1 provides an interactive visual interface for topology optimization from natural language.

Problem	GT $C$	LLM $C$	Penalty	Config
cantilever_basic	63.69	63.69	0.0%	6/6 ✓
mbb_beam	185.16	186.24	+0.6%	6/6 ✓
bridge	17.95	—	FAIL †	5/6 ✓
cantilever_hole	76.24	76.24	0.0%	6/6 ✓
deep_beam_shear	5.50	5.50	0.0%	6/6 ✓
simply_supported	12.88	13.86	+7.7%	6/6 ✓

Table 3: Configuration accuracy: ground-truth (GT) vs. LLM-configured compliance. Both use the LLM controller with 300 iterations. Config reports the number of matching specification fields (out of 6).

Panel of Figure 5 — Figure 5: Configuration accuracy ( table 3 ): ground-truth (GT) vs. LLM-configured topologies, both solved with the schedule controller at 300 iterations. The first three pairs are visually identical (0.0–0.6% penalty). The simply supported beam shows minor differences (+7.7%). The L-bracket is the one genuine outlier (+119%): the configurator placed the load at a different y-coordinate, producing a structurally different topology.

Controller	Pass%	Mean $C$	Med. $C$	Mean $\mathcal{G}$	Mean $t$ (s)
LLM agent	76.5%	159.60	76.24	0.000	130.0
Schedule	100%	170.10	77.35	0.000	106.2
Expert	88.2%	161.00	76.44	0.000	122.1
Three-field	88.2%	161.28	76.75	0.000	117.3
Tail-only	100%	452.62	211.78	0.002	22.9
Fixed	35.3%	175.73	86.74	0.169	91.0

Table 4: Controller comparison (summary): 17 2-D problems, 300 iterations, seed 42. All controllers share an identical 40-iteration STANDARD_TAIL.

Standard benchmarks
Problem	LLM	Schedule	Expert	Three-field	Tail-only	Fixed
cantilever_60 $\times$ 30	63.69	64.46	63.13	63.27	141.17	68.54
cantilever_120 $\times$ 40	171.65	177.42	172.63	173.80	580.81	181.03
mbb_90 $\times$ 30	185.16	203.11	190.34	191.07	337.66	204.81
mbb_150 $\times$ 50	186.05	202.12	188.12	189.22	309.73	196.80
Volume-fraction variations

Table 5: Per-problem compliance matrix: 17 2-D problems

\times

6 controllers, 300 iterations, seed 42. Best compliance per problem in bold ; ties are bolded for all matching controllers. All controllers except Fixed share an identical 40-iteration STANDARD_TAIL (Fixed has no tail).

Panel of Figure 6 — Figure 6: Controller comparison ( table 4 ): optimized topologies for four representative problems across five controllers. The LLM, schedule, and expert controllers produce crisp, structurally similar topologies. The fixed controller retains gray intermediate densities. The tail-only controller — which receives no exploration and starts the tail from uniform density — produces bloated, fragmented designs with $2$ – $30\times$ higher compliance, confirming that the exploration phase is essential. Black = solid, white = void.

Figure 7: Compliance convergence on the cantilever 60 $\times$ 30 benchmark. (a) Active controllers on a linear scale: the LLM agent (blue) maintains higher compliance during the exploration phase (iterations 0–120) before converging in the tail. The schedule (red) and expert (green) converge earlier. All active controllers reach similar final compliance ( $\approx$ 63–65). (b) All controllers on a log scale: the tail-only controller (brown) spikes to $3.5\times 10^{6}$ during the tail phase as it attempts to build structure from uniform density, before settling at $C=141$ — $2.2\times$ worse than the active controllers.

Problem	LLM	Schedule	Expert	Three-field	Tail-only	Fixed
cantilever_3d	4.82	4.87	4.83	4.83	14.23	6.31
mbb_3d	7.61	7.77	7.63	7.64	9.49	9.67

Table 6: 3-D controller comparison: 30

\times

\times

8 mesh,

V_{f}=0.4

, 300 iterations.

Panel of Figure 8 — Figure 8: 3-D cantilever (30 $\times$ 15 $\times$ 8, $V_{f}=0.4$ ): isosurface renders (top, marching cubes at $\rho=0.5$ ) and X-ray density projections (bottom, mean along each axis). The LLM and schedule controllers produce clean wedge-shaped cantilevers with material concentrated at the top and bottom flanges. The tail-only controller produces a bloated slab with internal voids — $3\times$ higher compliance. The fixed controller retains gray intermediate densities visible in the washed-out X-ray projections.

Panel of Figure 9 — Figure 9: Interactive web demo: 3-D cantilever workflow. Left: problem configuration with editable domain, mesh, loads, supports, and solver parameters. Right: optimized topology with interactive 3-D visualisation, eight-check evaluator, and LLM-generated qualitative assessment. This demonstrates the complete autonomous pipeline operating on a 3-D problem through the browser interface — a capability absent from all systems in Table 1 .

Metric	Value
Single-shot pass rate	10/10 (100%)
With-retries pass rate	10/10 (100%)
Mean attempts needed	1.0

Table 7: Retry recovery: 10 pipeline problems, schedule controller, 300 iterations, LLM-configured specifications.

Topology Optimization

Topology optimization finds material layouts that meet performance and manufacturing constraints across engineering systems.

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Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization

Shaoliang Yang, Jun Wang, Yunsheng Wang

Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA

Topology Optimization Large Language Model-Guided Optimization Language Model-Based Control

Open paper AskPDF arXiv

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\%

-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.

Abstract

Topology Optimization

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