Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

PACE: Pacing Operator Learning to Accurate Optical Field Simulation for Complicated Photonic Devices

Hanqing Zhu, Wenyan Cong, Guojin Chen, Shupeng Ning, Ray T. Chen, Jiaqi Gu, David Z. Pan

TL;DR

This work proposes a novel cross-axis factorized PACE operator with a strong long-distance modeling capacity to connect the full-domain complex field pattern with local device structures and boosts the prediction fidelity to an unprecedented level for simulating complex photonic devices with a novel operator design driven by the above challenges.

Abstract

Electromagnetic field simulation is central to designing, optimizing, and validating photonic devices and circuits. However, costly computation associated with numerical simulation poses a significant bottleneck, hindering scalability and turnaround time in the photonic circuit design process. Neural operators offer a promising alternative, but existing SOTA approaches, NeurOLight, struggle with predicting high-fidelity fields for real-world complicated photonic devices, with the best reported 0.38 normalized mean absolute error in NeurOLight. The inter-plays of highly complex light-matter interaction, e.g., scattering and resonance, sensitivity to local structure details, non-uniform learning complexity for full-domain simulation, and rich frequency information, contribute to the failure of existing neural PDE solvers. In this work, we boost the prediction fidelity to an unprecedented level for simulating complex photonic devices with a novel operator design driven by the above challenges. We propose a novel cross-axis factorized PACE operator with a strong long-distance modeling capacity to connect the full-domain complex field pattern with local device structures. Inspired by human learning, we further divide and conquer the simulation task for extremely hard cases into two progressively easy tasks, with a first-stage model learning an initial solution refined by a second model. On various complicated photonic device benchmarks, we demonstrate one sole PACE model is capable of achieving 73% lower error with 50% fewer parameters compared with various recent ML for PDE solvers. The two-stage setup further advances high-fidelity simulation for even more intricate cases. In terms of runtime, PACE demonstrates 154-577x and 11.8-12x simulation speedup over numerical solver using scipy or highly-optimized pardiso solver, respectively. We open sourced the code and dataset.

PACE: Pacing Operator Learning to Accurate Optical Field Simulation for Complicated Photonic Devices

TL;DR

This work proposes a novel cross-axis factorized PACE operator with a strong long-distance modeling capacity to connect the full-domain complex field pattern with local device structures and boosts the prediction fidelity to an unprecedented level for simulating complex photonic devices with a novel operator design driven by the above challenges.

Abstract

Electromagnetic field simulation is central to designing, optimizing, and validating photonic devices and circuits. However, costly computation associated with numerical simulation poses a significant bottleneck, hindering scalability and turnaround time in the photonic circuit design process. Neural operators offer a promising alternative, but existing SOTA approaches, NeurOLight, struggle with predicting high-fidelity fields for real-world complicated photonic devices, with the best reported 0.38 normalized mean absolute error in NeurOLight. The inter-plays of highly complex light-matter interaction, e.g., scattering and resonance, sensitivity to local structure details, non-uniform learning complexity for full-domain simulation, and rich frequency information, contribute to the failure of existing neural PDE solvers. In this work, we boost the prediction fidelity to an unprecedented level for simulating complex photonic devices with a novel operator design driven by the above challenges. We propose a novel cross-axis factorized PACE operator with a strong long-distance modeling capacity to connect the full-domain complex field pattern with local device structures. Inspired by human learning, we further divide and conquer the simulation task for extremely hard cases into two progressively easy tasks, with a first-stage model learning an initial solution refined by a second model. On various complicated photonic device benchmarks, we demonstrate one sole PACE model is capable of achieving 73% lower error with 50% fewer parameters compared with various recent ML for PDE solvers. The two-stage setup further advances high-fidelity simulation for even more intricate cases. In terms of runtime, PACE demonstrates 154-577x and 11.8-12x simulation speedup over numerical solver using scipy or highly-optimized pardiso solver, respectively. We open sourced the code and dataset.

Paper Structure

This paper contains 30 sections, 2 theorems, 10 equations, 13 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Neural Operators for PDE
  4. Optical Field Simulation with Machine Learning
  5. Understand the Problem Setup and Challenge
  6. Challenges in Predicting the Light Field of Complicated Photonic Devices
  7. Proposed PACE Methods
  8. Parameter-efficient and Effective Cross-axis Factorized PACE Operator
  9. Cascaded Learning from Rough to Clear
  10. Experimental Results
  11. Experimental Setup
  12. Main Results
  13. Prediction Quality of Single PACE Model
  14. Quality Improvement with Two-stage Model
  15. Speedup over Numerical Tools
  16. ...and 15 more sections

Key Result

Corollary 4.1

The factorized Fourier integral operator $\mathcal{K}$NN_ICLR2023_TranNP_Neurips2022_Gu factorizes the original Fourier integral operator NN_ICLR2021_Li along each dimension $n$ in the N-dimension domain $\Omega$, where each item explicitly computes a 1-D kernel integral, $\int_{\Omega_n}\kappa(\boldsymbol{r}_1, \boldsymbol{r}_2)^{n}v_k(\boldsymbol{r}_2)^{n}\text{d}v_k(\boldsymbol{r}_2)^{n}$. It

Figures (13)

  • Figure 1: Challenges of complicated optical device simulation: (a-d) and learning framework (e).
  • Figure 2: (a) PACE block with double skip and pre-normalization; (b) Our cross-axis factorized PACE operator.
  • Figure 3: Factorized FNO ML_ICLR2023_TranNP_Neurips2022_Gu.
  • Figure 4: The proposed cascaded learning flow with two stages. The first stage learns an initial and rough solution, followed by the second stage to revise it further. A cross-stage distillation path is used to transfer the learned knowledge from the first stage to the second stage.
  • Figure 5: Speedup of PACE over angler NP_ACSPhotonics2018_Lim using scipy (S)/ pardiso (P) with simulation granularity (0.05nm) and (0.075nm).
  • ...and 8 more figures

Theorems & Definitions (2)

  • Corollary 4.1
  • Corollary A.1