# Fast Neural Network based Solving of Partial Differential Equations

arXiv: https://arxiv.org/abs/2205.08978 · HTML: https://mlsanity.com/paper/2205.08978/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 18 May 2022.

## Builds on (most cited first, 4 of 4)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)

## Built on by (most cited first, 1 of 1)

- [LatentPINNs: Generative physics-informed neural networks via a latent representation learning](https://mlsanity.com/paper/2305.07671/) (2023)

## Abstract (arXiv)

We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to converge to a PDE solution much faster than classic Physically Informed Neural Network (PINNs) approaches.