Initialization-enhanced physics-informed neural network with domain decomposition (IDPINN)

We propose a new physics-informed neural network framework, IDPINN, which improves the prediction accuracy of PINNs through initialization and domain decomposition. First, we train a PINN on a small dataset to obtain an initial network structure, including weight matrices and bias vectors. This trained network is then used to initialize the PINNs for each sub-domain in the domain decomposition. Moreover, we impose a smoothness condition at the interface to further improve prediction performance. We numerically evaluated IDPINN on several forward problems and demonstrated its advantages.