TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
This addresses model reduction challenges in transport-dominated PDEs for computational physics and engineering, representing a novel paradigm rather than an incremental improvement.
The paper tackled nonlinear model order reduction for transport-dominated partial differential equations with parameter-dependent discontinuities, introducing TGPT-PINN, which incorporates a shock-capturing loss and transform layer to overcome linear reduction limitations, demonstrating effectiveness on nontrivial parametric PDEs.
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.