# WaveY-Net: Physics-augmented deep learning for high-speed electromagnetic simulation and optimization

arXiv: https://arxiv.org/abs/2203.01248 · HTML: https://mlsanity.com/paper/2203.01248/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 67 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [Data Augmentation for Low-Resource Neural Machine Translation](https://mlsanity.com/paper/1705.00440/) (2017)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data](https://mlsanity.com/paper/1808.04327/) (2018)
- [Global optimization of dielectric metasurfaces using a physics-driven neural network](https://mlsanity.com/paper/1906.04157/) (2019)

## Built on by (most cited first, 8 of 8)

- [XLB: A differentiable massively parallel lattice Boltzmann library in Python](https://mlsanity.com/paper/2311.16080/) (2023)
- [Towards General Neural Surrogate Solvers with Specialized Neural Accelerators](https://mlsanity.com/paper/2405.02351/) (2024)
- [Approximating the full-field temperature evolution in 3D electronic systems from randomized "Minecraft" systems](https://mlsanity.com/paper/2209.10369/) (2022)
- [Hybrid Modeling Design Patterns](https://mlsanity.com/paper/2401.00033/) (2023)
- [Photonic Structures Optimization Using Highly Data-Efficient Deep Learning: Application To Nanofin And Annular Groove Phase Masks](https://mlsanity.com/paper/2309.01995/) (2023)
- [A Physics-Informed Hierarchical Neural Network for Microwave Scattering Analysis of 3D PEC Targets](https://mlsanity.com/paper/2508.03774/) (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)

## Abstract (arXiv)

The calculation of electromagnetic field distributions within structured media is central to the optimization and validation of photonic devices. We introduce WaveY-Net, a hybrid data- and physics-augmented convolutional neural network that can predict electromagnetic field distributions with ultra fast speeds and high accuracy for entire classes of dielectric photonic structures. This accuracy is achieved by training the neural network to learn only the magnetic near-field distributions of a system and to use a discrete formalism of Maxwell's equations in two ways: as physical constraints in the loss function and as a means to calculate the electric fields from the magnetic fields. As a model system, we construct a surrogate simulator for periodic silicon nanostructure arrays and show that the high speed simulator can be directly and effectively used in the local and global freeform optimization of metagratings. We anticipate that physics-augmented networks will serve as a viable Maxwell simulator replacement for many classes of photonic systems, transforming the way they are designed.