In this paper we introduce a Meshfree Variational Physics Informed Neural Network. It is a Variational Physics Informed Neural Network that does not require the generation of a triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational Physics Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh.

翻译：本文提出一种无网格变分物理信息神经网络。该网络是一种无需生成全域三角剖分，且可通过自适应测试函数集进行训练的变分物理信息神经网络。为构建测试空间，我们利用后验误差指示器，仅在误差较高区域添加测试函数。本文提出并比较了四种训练策略。数值结果表明，相较于在准均匀网格上使用相同数量测试函数训练的变分物理信息神经网络，本方法具有更高的精度。