论文标题
通过变异物理信息的神经网络求解PDE：A后验分析
Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis
论文作者
论文摘要
我们考虑通过变异物理信息信息网络（VPINN）对椭圆边界值问题的离散化，其中测试函数是连续的，分段线性函数在域的三角测量上。我们定义了由残余术语，损耗项和数据振荡项制成的后验误差估计器。我们证明，估计器在控制精确和VPINN溶液之间误差的能量规范方面既可靠又有效。数值结果与理论预测非常吻合。
We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a posteriori error estimator, made of a residual-type term, a loss-function term, and data oscillation terms. We prove that the estimator is both reliable and efficient in controlling the energy norm of the error between the exact and VPINN solutions. Numerical results are in excellent agreement with the theoretical predictions.
