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 tha...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2024-10, Vol.430, p.117198, Article 117198
Main Authors: Chen, Yanlai, Ji, Yajie, Narayan, Akil, Xu, Zhenli
Format: Article
Language:English
Subjects:
Meta-learning
Nonlinear model order reduction
Parametric systems
Physics-informed neural networks
Reduced basis method
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Summary: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.
ISSN:0045-7825
DOI:10.1016/j.cma.2024.117198