Fast Neural Network based Solving of Partial Differential Equations

TL;DR

This paper introduces a new neural network method inspired by Neural Radiance Fields that significantly accelerates the process of solving partial differential equations compared to traditional PINNs.

Contribution

The paper proposes a novel neural network approach leveraging NeRFs to achieve faster convergence in solving PDEs, improving upon existing PINN methods.

Findings

Faster convergence to PDE solutions than classic PINNs

Effective application of NeRF-inspired neural networks for PDEs

Potential for real-time PDE solving in scientific computing

Abstract

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.