论文标题
弹性的物理信息神经网络解决方案的基于能量的误差限制
Energy-based error bound of physics-informed neural network solutions in elasticity
论文作者
论文摘要
为弹性问题的物理信息神经网络解决方案提出了基于能量的后验误差。可允许的位移应力解溶液对从物理信息的混合形式的神经网络获得，并且所提出的误差结合被配制为解决方案对定义的本构关系误差。这样的误差估计器提供了神经网络离散化的全局误差的上限。在一个例子中研究了界限以及物理信息神经网络解决方案的渐近行为。
An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstrating example.
