When solving partial differential equations (PDEs), traditional Physics-Informed Neural Networks (PINNs) often encounter difficulties in capturing critical physical features and addressing information bias between subdomains. To overcome these limitations, this paper proposes a Dual Adaptive Domain Decomposition Physics-Informed Neural Network (DADD-PINN). The core of this method lies in the construction of a dual-driven architecture that facilitates intra-subdomain feature extraction and inter-subdomain feature coordination. Within each subdomain, the solver’s precision is significantly enhanced by integrating a multi-criterion adaptive sampling strategy with a dynamic weighting mechanism. Experimental results demonstrate that DADD-PINN reduces the optimal L2 error by 1–2 orders of magnitude compared to existing baselines. The model exhibits superior generalization and robustness across various physical fields, offering a new route toward accurate and efficient solutions for complex PDEs.
Xiong et al. (Mon,) studied this question.