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PACE: Pacing Operator Learning to Accurate Optical Field Simulation for Complicated Photonic Devices
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Proposes PACE, a cross-axis factorized Fourier neural operator with a two-stage rough-to-refined cascade for high-fidelity electromagnetic field simulation of complicated photonic devices.
Problem
Neural operators for optical field simulation (Maxwell PDE) of real-world complicated photonic devices remain inaccurate (NeurOLight reports 0.38 normalized MAE on etched MMI), due to multi-scale light-matter interaction, sensitivity to local structure, non-uniform learning difficulty, and rich freq
Approach
A cross-axis factorized integral kernel (PACE operator) computed via FFTs along horizontal and vertical axes with grouping, an explicit high-frequency projection unit, and an instance-based self-weighted path; plus a two-stage cascade where stage I predicts a rough field and stage II refines it with cross-stage feature distillation.
Key results
- PACE 12-layer (1.71M params) reaches test error 10.59e-2 on Etched MMI 3x3 vs 17.21e-2 for NeurOLight (16-layer, 2.11M), and 2.82e-2 on Metaline 3x3 vs 6.09e-2 for NeurOLight.
- Averaged over benchmarks, PACE shows 73.85% lower test error than all baselines with 51.67% fewer parameters.
- Two-stage PACE-I + PACE-II with cross-stage distillation reduces Etched MMI 3x3 test error to 5.32e-2 (20-layer single model: 7.04e-2).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PACE instead of NeurOLight | Optical field simulation · Etched MMI 3x3 | test error (10^-2): 17.21 -> 10.59 | Helped |
| Use PACE instead of NeurOLight | Optical field simulation · Etched MMI 5x5 | test error (10^-2): 17.41 -> 11.91 | Helped |
| Use PACE instead of NeurOLight | Optical field simulation · Metaline 3x3 | test error (10^-2): 6.09 -> 2.82 | Helped |
| Add cross-stage feature distillation (ablation) | PACE-I + PACE-II · Etched MMI 3x3 | test error (10^-2): 5.83 -> 5.32 | Helped |
| Add cross-stage feature distillation (ablation) | PACE-I + PACE-II · Etched MMI 5x5 | test error (10^-2): 6.78 -> 6.15 | Helped |
| Add a self-weighted path (ablation) | 8-layer PACE · Metaline 3x3 | test error (10^-2): 5.66 -> 4.82 | Helped |
| Add the high-frequency projection unit (ablation) | 8-layer PACE · Metaline 3x3 | test error (10^-2): 5.97 -> 4.82 | Helped |
| Replace the cross-axis factorized integral kernel with TFNO (ablation) | 8-layer PACE · Metaline 3x3 | test error (10^-2): 4.82 -> 9.51 | Hurt |
| Set the group number to 1 instead of 4 (ablation) | 8-layer PACE · Metaline 3x3 | test error (10^-2): 4.82 -> 4.55 | Helped |
| Set the group number to 2 instead of 4 (ablation) | 8-layer PACE · Metaline 3x3 | test error (10^-2): 4.82 -> 4.80 | Helped |
| Increase the single-stage model from 12 to 20 layers (ablation) | PACE · Etched MMI 3x3 | test error (10^-2): 10.59 -> 7.04 | Helped |
| Use a two-stage PACE-I + PACE-II model with cross-stage distillation instead of a 20-layer single-stage model (ablation) | PACE · Etched MMI 3x3 | test error (10^-2): 7.04 -> 5.32 | Helped |
Surprising findings
- Scaling a single PACE model from 12 to 20 layers gives less improvement than the two-stage cascade, consistent with saturation of deeper single models.
Limitations
- Only steady-state FDFD simulations were studied; FDTD not explored.
- FFT kernels on GPU are not fully optimized.
- Out-of-C-band wavelengths show 10-15% error without sampled wavelengths in training.
Experimental setup
Datasets: Etched MMI 3x3 Etched MMI 5x5 Metaline 3x3
Benchmarks: Etched MMI 3x3 Etched MMI 5x5 Metaline 3x3
Metrics: normalized MSE (test error) train error number of parameters runtime speedup
Baselines: NeurOLight FNO-2d Factorized FNO-2d Tensorized FNO-2d U-NO Latent spectral method UNet Dil-ResNet Attention-based model
Builds on: Fourier neural operator Factorized FNO NeurOLight
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