# Deep-learning PDEs with unlabeled data and hardwiring physics laws

arXiv: https://arxiv.org/abs/1904.06578 · HTML: https://mlsanity.com/paper/1904.06578/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Physics-informed neural networks for diffraction tomography](https://mlsanity.com/paper/2207.14230/) (2022)
- [Optical Diffraction Tomography based on 3D Physics-Inspired Neural Network (PINN)](https://mlsanity.com/paper/2206.05236/) (2022)

## Abstract (arXiv)

Providing fast and accurate solutions to partial differential equations is a problem of continuous interest to the fields of applied mathematics and physics. With the recent advances in machine learning, the adoption learning techniques in this domain is being eagerly pursued. We build upon earlier works on linear and homogeneous PDEs, and develop convolutional deep neural networks that can accurately solve nonlinear and non-homogeneous equations without the need for labeled data. The architecture of these networks is readily accessible for scientific disciplines who deal with PDEs and know the basics of deep learning.