Structure Preserving PINN for Solving Time Dependent PDEs with Periodic Boundary
<|reference_start|>Structure Preserving PINN for Solving Time Dependent PDEs with Periodic Boundary: We present a structure preserving PINN for solving a series of time dependent PDEs with periodic boundary. Our method can incorporate the periodic boundary condition as the natural output of any deep neural net, hence significantly improving the training accuracy of baseline PINN. Together with mini-batching and other PINN variants (SA-PINN, RBA-PINN, etc.), our structure preserving PINN can even handle stiff PDEs for modeling a wide range of convection-diffusion and reaction-diffusion processes. We demonstrate the effectiveness of our PINNs on various PDEs from Allen Cahn, Gray Scott to nonlinear Schrodinger.<|reference_end|>
@article{hao2024structure,
    title={Structure Preserving PINN for Solving Time Dependent PDEs with Periodic
  Boundary},
    author={Baoli Hao, Ulisses Braga-Neto, Chun Liu, Lifan Wang, Ming Zhong},
    journal={arXiv preprint arXiv:2404.16189},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16189},
    primaryClass={math.NA cs.NA}
}