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.

我们介绍了转换生成式预训练物理信息神经网络 (TGPT-PINN)，用于在 MOR 整合 PINNs 框架中完成非线性模型降阶的任务。通过引入用于捕捉震荡的损失函数组件以及参数相关的转换层，TGPT-PINN 克服了传输主导区域中线性模型降阶的限制。我们通过多个复杂的参数化偏微分方程在 PINNs 框架中展示了这一新的非线性模型降阶能力。