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In this paper, we propose the augmented physics-informed neural network (APINN), which adopts soft and trainable domain decomposition and flexible parameter sharing to further improve the extended PINN (XPINN) as well as the vanilla PINN methods.
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Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
Ameya D Jagtap and George Em Karniadakis · 2020
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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Ameya D Jagtap, Ehsan Kharazmi, and George Em Karniadakis · 2020
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Xuhui Meng, Zhen Li, Dongkun Zhang, and George Em Karniadakis · 2020
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Error analysis for physics informed neural networks (pinns) approximating kolmogorov pdes
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Zheyuan Hu, Ameya D Jagtap, George Em Karniadakis, and Kenji Kawaguchi · 2021
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Anonymous · 2022
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A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
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