TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs

arXiv:2403.03459v1 Announce Type: cross
Abstract: 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 …

abstract arxiv building cs.lg cs.na design development differential framework generative gpt math.na network networks neural networks nonlinear model physics physics-informed pinn test transport type