TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
Yanlai Chen Yajie Ji Akil Narayan Zhenli Xu
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.