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Deep Electromagnetic Structure Design Under Limited Evaluation Budgets
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Proposes Progressive Quadtree-based Search (PQS), combining a quadtree representation that grows the design space gradually with consistency-based (Kendall's tau) sample selection, to design electromagnetic structures under a ~1000-simulation budget.
Problem
Electromagnetic structure design involves a huge binary design space (~10^86-10^90) and costly full-wave simulations, and existing predictor- or generator-based methods need thousands of labeled samples, which is impractical under tight evaluation budgets.
Approach
Represent the layout as a quadtree so the search starts in a low-dimensional space and progressively refines to finer resolution, and use the Kendall's tau consistency between successive predictors to split each batch between predictor-ranked exploitation and random exploration.
Key results
- On DualFSS with 1000 simulations, PQS reaches Agg Obj 15.20 dB versus 7.28 dB for random sampling and 8.93 dB for cVAE (7000 simulations).
- On HGA with 1000 simulations, PQS reaches Agg Obj 3.66 dB, above all baselines (best baseline InvGrad 3.18 dB with 4000 simulations).
- In robustness tests on a surrogate-replaced HGA simulator over 10 runs, PQS achieves 4.34 ± 0.34 Agg Obj versus -0.29 ± 0.40 for the best baseline SAHSO.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PQS instead of RS | DualFSS · DualFSS | Agg Obj: 7.2824 -> 15.1964 | Helped |
| use PQS instead of the strongest baseline cVAE | DualFSS · DualFSS | Agg Obj: 8.9294 -> 15.1964 | Helped |
| use PQS instead of InvGrad | High-gain Antenna · High-gain Antenna | Agg Obj: 3.1783 -> 3.6595 | Helped |
| use PQS instead of Surrogate-RS | High-gain Antenna · High-gain Antenna | Agg Obj: 3.0857 -> 3.6595 | Helped |
| increase Nmax from 16 to 32 (ablation) | PQS · High-gain Antenna | Agg Obj: 3.0867 -> 3.6595 | Helped |
| increase Nmax from 32 to 64 (ablation) | PQS · High-gain Antenna | Agg Obj: 3.6595 -> 3.0233 | Hurt |
| add QSS to the variant without QSS or CSS (ablation) | PQS · High-gain Antenna | Agg Obj: 3.0857 -> 3.2209 | Helped |
| add CSS to PQS with QSS (ablation) | PQS · High-gain Antenna | Agg Obj: 3.2209 -> 3.6595 | Helped |
| replace CSS sample selection with Top-K selection (ablation) | PQS · High-gain Antenna | search efficiency: +50% | Hurt |
Surprising findings
- Surrogate-assisted predictor methods (e.g., Surrogate-RS on DualFSS at 5.81 dB) underperform plain random sampling (7.28 dB) under a 1000-sample budget.
- Smaller quadtree variable limit (N=16) gives the highest Kendall's tau predictor accuracy, yet N=32 gives the best final objective.
Limitations
- Robustness study replaces the real simulator with a surrogate (KTau 0.7969 to real simulations), not full-wave simulation.
- Several baselines were re-implemented by the authors with custom adaptations, so comparisons depend on those choices.
- Evaluated only on two EMS tasks, both with two objectives.
Experimental setup
Datasets: DualFSS simulation samples High-gain Antenna simulation samples (37,354 samples used for surrogate in robustness study)
Benchmarks: Dual-layer Frequency Selective Surface (DualFSS) High-gain Antenna (HGA)
Metrics: Agg Obj (min over objectives, dB) Obj1 Obj2 number of simulations Kendall's tau
Baselines: Random Sampling Surrogate-RS Surrogate-GA Surrogate-GW TS-DDEO SAHSO cGAN cVAE IDN InvGrad GenCO
Builds on: surrogate-assisted optimization Kendall's tau
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