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arXiv · 2403.03459

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

Yanlai Chen·Yajie Ji·Akil Narayan·Zhenli Xu
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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 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.

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Yanlai Chen, Yajie Ji, Akil Narayan, Zhenli Xu. 2024-03-06. TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs. https://arxiv.org/abs/2403.03459

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