TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
<|reference_start|>TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs: We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework. Building on the recent development of the GPT-PINN that is a network-of-networks design achieving snapshot-based model reduction, we design and test a novel paradigm for nonlinear model reduction that can effectively tackle problems with parameter-dependent discontinuities. Through incorporation of a shock-capturing loss function component as well as a parameter-dependent transform layer, the TGPT-PINN overcomes the limitations of linear model reduction in the transport-dominated regime. We demonstrate this new capability for nonlinear model reduction in the PINNs framework by several nontrivial parametric partial differential equations.<|reference_end|>
@article{chen2024tgpt-pinn:,
    title={TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs},
    author={Yanlai Chen, Yajie Ji, Akil Narayan, Zhenli Xu},
    journal={arXiv preprint arXiv:2403.03459},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.03459},
    primaryClass={math.NA cs.LG cs.NA}
}