Preprint · arXiv:2107.09443 2021
NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations
arXiv:2107.09443, 2021
Abstract
Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the various methodologies of PINNs and showcase the various types of problems a PINN software can solve. We then detail the inner workings of NeuralPDE.jl and show how a formulation structured around numerical quadrature gives rise to new loss functions which allow for adaptivity towards bounded error tolerances.
We showcase how NeuralPDE uses a purely symbolic formulation so that all of the underlying training code is generated from an abstract formulation, and show how to make use of GPUs and solve systems of PDEs. We end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman (DFN) Model, and showcase how this PDE can be formulated and solved with NeuralPDE.
The full text is available as a PDF; the version of record is at doi:10.48550/arXiv.2107.09443.
Cite this paper
Download .bib ↓Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Lujan, Valentin Sulzer, Ashutosh Bharambe and et al., “NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations,” arXiv:2107.09443, 2021.
doi:10.48550/arXiv.2107.09443
@article{zubov2021neuralpde,
title={{NeuralPDE}: Automating Physics-Informed Neural Networks ({PINNs}) with Error Approximations},
author={Zubov, Kirill and McCarthy, Zoe and Ma, Yingbo and Calisto, Francesco and Pagliarino, Valerio and Azeglio, Simone and Bottero, Luca and Luj{\'{a}}n, Emmanuel and Sulzer, Valentin and Bharambe, Ashutosh and others},
journal={arXiv preprint arXiv:2107.09443},
year={2021},
url={https://arxiv.org/abs/2107.09443},
doi={10.48550/arXiv.2107.09443}
}