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math.NA2025
Derivative-informed Graph Convolutional Autoencoder with Phase Classification for the Lifshitz-Petrich Model
Yanlai Chen, Yajie Ji, Zhenli Xu
The Lifshitz-Petrich (LP) model is a classical model for describing complex spatial patterns such as quasicrystals and multiphase structures. Solving and classifying the solutions…
math.NA2025
EGPT-PINN: Entropy-enhanced Generative Pre-Trained Physics Informed Neural Networks for parameterized nonlinear conservation laws
Yajie Ji, Yanlai Chen, Zhenli Xu
We propose an entropy-enhanced Generative Pre-Trained Physics-Informed Neural Network with a transform layer (EGPT-PINN) for solving parameterized nonlinear conservation laws. The…
math.NA2024
TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
Yanlai Chen, Yajie Ji, Akil Narayan +1
We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated part…