PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks

This branch contains the code for paper: PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks

Usage

The usage instructions for this branch are consistent with those in the main branch. Please refer to the main branch documentation for detailed setup and execution guidelines.

Benchmarks

The following table shows the performance of PirateNets compared to JAX-PI on a set of benchmark problems. The accuracy is measured in relative $L^2$ error between the predicted and true solutions.

Benchmark	PirateNet	JAX-PI
Allen-Cahn	$2.24 \times 10^{−5}$	$5.37 \times 10^{−5}$
Korteweg–De Vries	$4.27 \times 10^{−4}$	$1.96 \times 10^{−3}$
Gray-Scott	$3.61 \times 10^{−3}$	$6.13$
Ginzburg-Landau	$1.49 \times 10^{−2}$	$3.20 \times 10^{−2}$
Lid-driven cavity flow (Re=3200)	$4.21 \times 10^{−2}$	$1.58 \times 10^{−1}$

Grey-Scott

Ginzburg–Landau

Citation

@article{wang2024piratenets,
  title={PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks},
  author={Wang, Sifan and Li, Bowen and Chen, Yuhan and Perdikaris, Paris},
  journal={arXiv preprint arXiv:2402.00326},
  year={2024}
}