# A neural operator-based surrogate solver for free-form electromagnetic inverse design

arXiv: https://arxiv.org/abs/2302.01934 · HTML: https://mlsanity.com/paper/2302.01934/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 73 references that are in the map.
- First posted on arXiv 4 Feb 2023.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport](https://mlsanity.com/paper/2204.06684/) (2022)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [Active learning of deep surrogates for PDEs: Application to metasurface design](https://mlsanity.com/paper/2008.12649/) (2020)
- [Physics-enhanced deep surrogates for partial differential equations](https://mlsanity.com/paper/2111.05841/) (2021)
- [Inverse design of photonic crystals through automatic differentiation](https://mlsanity.com/paper/2003.00379/) (2020)
- [Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction](https://mlsanity.com/paper/1809.06674/) (2018)

## Built on by (most cited first, 19 of 19)

- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2510.25803/) (2025)
- [Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling](https://mlsanity.com/paper/2401.09516/) (2024)
- [Inverse Design in Nanophotonics via Representation Learning](https://mlsanity.com/paper/2507.00546/) (2025)
- [Learning Electromagnetic Metamaterial Physics With ChatGPT](https://mlsanity.com/paper/2404.15458/) (2024)
- [PIC2O-Sim: A Physics-Inspired Causality-Aware Dynamic Convolutional Neural Operator for Ultra-Fast Photonic Device FDTD Simulation](https://mlsanity.com/paper/2406.17810/) (2024)
- [Ambient Physics: Training Neural PDE Solvers with Partial Observations](https://mlsanity.com/paper/2602.13873/) (2026)
- [PearSAN: A Machine Learning Method for Inverse Design using Pearson Correlated Surrogate Annealing](https://mlsanity.com/paper/2412.19284/) (2024)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Photonic Structures Optimization Using Highly Data-Efficient Deep Learning: Application To Nanofin And Annular Groove Phase Masks](https://mlsanity.com/paper/2309.01995/) (2023)
- [Generalizing Deep Surrogate Solvers for Broadband Electromagnetic Field Prediction at Unseen Wavelengths](https://mlsanity.com/paper/2408.02971/) (2024)
- [Operator Learning for Schr"odinger Equation: Unitarity, Error Bounds, and Time Generalization](https://mlsanity.com/paper/2505.18288/) (2025)
- [Optimizing Predictive Maintenance in Intelligent Manufacturing: An Integrated FNO-DAE-GNN-PPO MDP Framework](https://mlsanity.com/paper/2511.05594/) (2025)
- [Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonics](https://mlsanity.com/paper/2602.18148/) (2026)
- [Alpha-RF: Automated RF-Filter-Circuit Design with Neural Simulator and Reinforcement Learning](https://mlsanity.com/paper/2603.00104/) (2026)
- [Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data](https://mlsanity.com/paper/2605.20514/) (2026)
- [Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problems](https://mlsanity.com/paper/2608.17344/) (2026)
- [Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments](https://mlsanity.com/paper/2608.29907/) (2026)
- [Neural Surrogate Modeling of Ultrasonic Wave Propagation in Heterogeneous Media](https://mlsanity.com/paper/2610.13258/) (2026)

## Abstract (arXiv)

Neural operators have emerged as a powerful tool for solving partial differential equations in the context of scientific machine learning. Here, we implement and train a modified Fourier neural operator as a surrogate solver for electromagnetic scattering problems and compare its data efficiency to existing methods. We further demonstrate its application to the gradient-based nanophotonic inverse design of free-form, fully three-dimensional electromagnetic scatterers, an area that has so far eluded the application of deep learning techniques.