Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology. (arXiv:2211.08939v2 [cs.LG] UPDATED)

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. In particular, a trainable gate network is employed to
mimic the hard decomposition of XPINN, which can be flexibly fine-tuned for
discovering a potentially better partition. It weight-averages several sub-nets
as the output of APINN. APINN does not require complex interface conditions,
and its …

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