# Notes on Perfectly Matched Layers (PMLs)

arXiv: https://arxiv.org/abs/2108.05348 · HTML: https://mlsanity.com/paper/2108.05348/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2021.

## Built on by (most cited first, 4 of 4)

- [Neumann Series-based Neural Operator for Solving Inverse Medium Problem](https://mlsanity.com/paper/2409.09480/) (2024)
- [A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems](https://mlsanity.com/paper/2210.09228/) (2022)
- [Taming Waves: A Physically-Interpretable Machine Learning Framework for Realizable Control of Wave Dynamics](https://mlsanity.com/paper/2312.09460/) (2023)
- [Acoustic Wave Manipulation Through Sparse Robotic Actuation](https://mlsanity.com/paper/2502.08784/) (2025)

## Abstract (arXiv)

This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex stretched-coordinate viewpoint, and also discusses the limitations of PML.