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

arXiv: https://arxiv.org/abs/2411.03527 · HTML: https://mlsanity.com/paper/2411.03527/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 21 of 21)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020)
- [Solving High-Dimensional PDEs with Latent Spectral Models](https://mlsanity.com/paper/2301.12664/) (2023)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [FlashFFTConv: Efficient Convolutions for Long Sequences with Tensor Cores](https://mlsanity.com/paper/2311.05908/) (2023)
- [NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device Simulation](https://mlsanity.com/paper/2209.10098/) (2022)
- [Lightening-Transformer: A Dynamically-operated Optically-interconnected Photonic Transformer Accelerator](https://mlsanity.com/paper/2305.19533/) (2023)
- [A compact butterfly-style silicon photonic-electronic neural chip for hardware-efficient deep learning](https://mlsanity.com/paper/2111.06705/) (2021)
- [M3ICRO: Machine Learning-Enabled Compact Photonic Tensor Core based on PRogrammable Multi-Operand Multimode Interference](https://mlsanity.com/paper/2305.19505/) (2023)
- [Fuse and Mix: MACAM-Enabled Analog Activation for Energy-Efficient Neural Acceleration](https://mlsanity.com/paper/2208.08099/) (2022)
- [Integrated multi-operand optical neurons for scalable and hardware-efficient deep learning](https://mlsanity.com/paper/2305.19592/) (2023)
- [Dilated convolution neural operator for multiscale partial differential equations](https://mlsanity.com/paper/2408.00775/) (2024)

## Built on by (most cited first, 5 of 5)

- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [MAPS: Multi-Fidelity AI-Augmented Photonic Simulation and Inverse Design Infrastructure](https://mlsanity.com/paper/2503.01046/) (2025)
- [Democratizing Electronic-Photonic AI Systems: An Open-Source AI-Infused Cross-Layer Co-Design and Design Automation Toolflow](https://mlsanity.com/paper/2601.00130/) (2025)
- [Harnessing Photonics for Machine Intelligence](https://mlsanity.com/paper/2604.10841/) (2026)
- [Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data](https://mlsanity.com/paper/2605.20514/) (2026)

## Abstract (arXiv)

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.