Automatically imposing boundary conditions for boundary value problems by unified physics-informed neural network
Engineering with Computers - Trang 1-23 - 2023
Tóm tắt
Exact boundary conditions (BCs) imposition technique is widely used in physics-informed neural networks (PINNs) for solving boundary value problems (BVPs). In this regard, the selection of trial function satisfying essential BCs becomes hard to determine when complex geometric domain or essential BCs are considered. To address this challenge, an unified physics-informed neural network (UPINN) model is developed, in which the trial function is fully provided by deep neural networks (DNNs). The UPINN is a combination of two phases being implemented sequentially. The first one is to find DNN-based trial functions satisfying essential BCs in homogeneous form using loss function regulating the corresponding BCs. Then, the remaining one is to solve BVPs based on their strong or weak (variational) forms, in which the exact BCs imposition procedure is employed to constrain network outputs using the UPINN trial functions obtained from the first phase. The advantages of the proposed UPINN are demonstrated in terms of prediction accuracy and training cost for several solid mechanics problems with different BCs, even for complicated ones that restrict the regular PINNs significantly.
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