A Self-Evolving Agentic Framework for Metasurface Inverse Design

Yi Huang; Bowen Zheng; Yunxi Dong; Hong Tang; Huan Zhao; S. M. Rakibul Hasan Shawon; Hualiang Zhang

cs.AIApr 1, 2026

A Self-Evolving Agentic Framework for Metasurface Inverse Design

Authors: Yi Huang, Bowen Zheng, Yunxi Dong, Hong Tang, Huan Zhao, S. M. Rakibul Hasan Shawon, Hualiang Zhang

Organizations: Department of Electrical and Computer Engineering, University of Massachusetts Lowell

Abstract

Metasurface inverse design can realize complex optical functionality, but turning a target optical response into executable optimization code still requires substantial expertise in computational electromagnetics and solver-specific software engineering. We present a self-evolving agentic framework that lowers this barrier by coupling a coding agent, explicit human-readable skill files, and a deterministic physics-based evaluator. Rather than updating model weights, it revises the skill files from solver-grounded feedback, while the base model and differentiable solver, which provides the physics simulation and gradients, stay fixed. On a multi-type benchmark, skill evolution raises same-type task success from 38% to 74%, the fraction of physical criteria met from 0.51 to 0.87, and reduces average attempts from 4.10 to 2.30. On two new-type families, success holds near ceiling on one (0.92 to 0.90) and rises from 0.20 to 0.90 on the other. Skill evolution offers a practical path toward autonomous and accessible inverse-design workflows.

Figures & tables

Figure 1: Overview of the self-evolving agentic framework for metasurface inverse design. The framework is organized as two decoupled layers: an upper code-generation layer, where a coding agent turns a natural-language request into a candidate optimization program guided by an evolving skill file ( SKILL.md ), and a lower physics layer, where a fixed differentiable solver performs the electromagnetic forward simulation and provides gradients, and an evaluator scores the result against the task criteria. The agent programs the fixed solver rather than replacing it, and the loop runs autonomously without a human in the loop. An inner loop retries the program when an evaluation fails, while an outer loop lets a meta-agent revise the skill file from per-task feedback, keeping the best version on validation; a passing design is released as the realized metasurface. The demonstrated solver is a differentiable RCWA implementation, TorchRDIT [ 8 ] .

Dataset	Condition	SG	SE	CPF	BM	Attempts
Same-type	Starter-skill baseline	38.0%	86.0%	0.510	-2.380	4.10
Same-type	Post-train	74.0%	100.0%	0.870	-2.281	2.30
Same-type	Delta	+36.0pp	+14.0pp	+0.360	+0.099	-1.80
New-type-A	Starter-skill baseline	92.0%	100.0%	0.960	-4.626	1.60
New-type-A	Post-train	90.0%	100.0%	0.950	-2.092	1.68
New-type-A	Delta	-2.0pp	+0.0pp	-0.010	+2.534	+0.08

Table 1: Test set performance: baseline (starter skill file) vs. post-train (evolved skills).

Figure 2: Outcomes of skill evolution across the three settings (Same-type, New-type-A, New-type-B), on held-out test tasks. (a) Self-evolution gain: each line traces SG from the starter skill to the evolved skill, with signed delta labels in percentage points. (b) Rescued vs. regressed: per setting, the number of tasks moving from failing to passing (teal, rescued) or passing to failing (red, regressed); the faded grey pool is the baseline-failing denominator. (c) Cost per task: box plots of total LLM spend per task (USD) for the starter and evolved skill in each setting.

Figure 3: Mechanism of skill evolution, one panel per setting (Same-type, New-type-A, New-type-B). Within each panel, the blue line is the validation success rate ( SG on the held-out validation family, right axis) across skill-evolution iterations; the skill evolution band shows the elitist search, where each node is a candidate skill file, an arrow marks a revision of the current best skill, and the star marks the iteration whose skill stays best on validation and becomes the final evolved skill; the stacked bars are the training-time error composition per iteration (left axis), with bar totals annotated. Because the loop keeps the best-on-validation skill and discards regressions, a later high-error candidate is a rejected exploration step, not a regression in the final skill. Infrastructure failures such as connection errors and timeouts are excluded. For New-type-B the seed marks the zero-shot baseline on the test families (its iteration 0 was scored there), whereas iterations 1 to 4 are on the validation family.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Family	Problem type	Design space	Criterion form
$G_{1}$	Single-condition reflective design	Low-dimensional periodic reflective geometry	$R(\lambda_{0};x)\geq\tau_{R}$
$G_{2}$	Dual-angle reflective design	Low-dimensional periodic reflective geometry	$\begin{aligned} R(\lambda_{0},\theta_{1};x)&\geq\tau_{R},\\ R(\lambda_{0},\theta_{2};x)&\geq\tau_{R}\end{aligned}$
$G_{3}$	Polarization-selective reflective design	Low-dimensional periodic reflective geometry	$\begin{aligned} R_{\mathrm{TE}}(\lambda_{0};x)&\geq\tau_{\mathrm{hi}},\\ R_{\mathrm{TM}}(\lambda_{0};x)&\leq\tau_{\mathrm{lo}}\end{aligned}$
$G_{4}$	Dual-wavelength reflective design	Low-dimensional periodic reflective geometry	$\begin{aligned} R(\lambda_{1};x)&\geq\tau_{R},\\ R(\lambda_{2};x)&\geq\tau_{R}\end{aligned}$
$G_{5}$	Plasmonic reflective design	Periodic reflective geometry in a plasmonic regime	$R(\lambda_{0};x)\geq\tau_{R}$
$G_{6}$	Transmissive phase-target metasurface design	Unit-cell geometry with family-dependent parameterization	$\begin{aligned} &T(\lambda_{0};x)\geq\tau_{T},\\ &d_{\mathbb{S}^{1}}(\phi(\lambda_{0};x),\phi^{\star})\leq\varepsilon_{\phi}\end{aligned}$

Appendix

Table S1: Abstract task-family taxonomy used to describe the benchmark in this work.

Setting	Split	Tasks	Family coverage	Interpretation
Same-type	Train	50	One sibling template from each of $G_{1}$ through $G_{6}$	Same-type training over all six primary families
Same-type	Validation	15	Held-out sibling of $G_{1}$ , plus $G_{\mathrm{aux}}$	Mild generalization check using closely related sibling templates
Same-type	Test	50	Held-out sibling templates from $G_{2}$ through $G_{6}$	Same-type test on sibling templates not used during training
New-type-A	Train	50	$G_{1}$ , $G_{2}$ , and $G_{3}$	Training restricted to single-condition, dual-angle, and polarization-selective reflection
New-type-A	Validation	15	$G_{4}$	Validation on an unseen dual-wavelength family
New-type-A	Test	50	$G_{5}$ , $G_{6}$ , and $G_{\mathrm{aux}}$	Family-heldout test across plasmonic and transmissive phase-target regimes

Appendix

Table S2: Abstract composition of the finalized splits for the three evaluation settings.

	Same-type		New-type-A		New-type-B
Row	SG (%)	CPF	SG (%)	CPF	SG (%)	CPF
Starter-skill baseline (test)	38	0.51	92	0.96	20	0.34
Iteration 1 (train / val)	48 / 100	0.58 / 1.00	52 / 100	0.61 / 1.00	92 / 13	0.96 / 0.23
Iteration 2 (train / val)	80 / 100	0.89 / 1.00	48 / 93	0.62 / 0.93	92 / 100	0.96 / 1.00
Iteration 3 (train / val)	80 / 100	0.90 / 1.00	42 / 80	0.44 / 0.80	92 / 100	0.96 / 1.00
Iteration 4 (train / val)	80 / 100	0.87 / 1.00	26 / 100	0.34 / 1.00	90 / 100	0.95 / 1.00

Appendix

Table S3: Training and validation dynamics across skill-evolution iterations, for the three settings.

Figure S5.1: Tool-call composition during skill evolution, by setting (columns: Same-type, New-type-A, New-type-B) and split (top row: training; bottom row: validation). Stacked bars give the per-task share of read, bash, and write tool calls at each iteration; the black line is the total calls per task (right axis) and the dashed line is the fixed starter-skill baseline. Read and bash calls correspond to exploration and write calls to revision, so a shift toward shorter, write-led cycles indicates less effort spent on broad search as the skill matures.

Category	Definition
Tensor Index OOB	Errors caused by invalid tensor indexing, shape mismatch, or out-of-bounds tensor access during candidate-program execution.
API Misuse	Errors caused by incorrect use of solver or optimization APIs, including invalid argument conventions and unsupported call patterns.
Gradient Error	Failures related to broken computational graphs, missing gradients, or invalid backward propagation through the optimization objective.
No Code / No Solution	Cases in which the Coding Agent fails to produce a complete executable candidate, or produces a candidate that never reaches a valid solution.
Excluded infrastructure failures	Connection errors, timeouts, and similar runtime-environment failures are excluded from Figure 3 because they are not directly attributable to the learned skill content.

Appendix

Table S4: Error categories used in the main error-analysis figure.

Snapshot	Source	Length	Primary role
starter skill	same-type run, starter-skill snapshot (iter0)	92 lines	Minimal TorchRDIT setup and execution pattern
Evolved skill	same-type run, archived selected snapshot (iter1)	218 lines	Structured task classification, failure-aware guidance, and reusable strategy selection

Appendix

Table S5: Representative skill snapshots used in the qualitative case study.

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