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.
翻译:对于弹性问题的物理知情神经网络解决方案,提出了基于能源的事后误差。从物理知情神经网络的混合形式中获得了可允许的偏移压力解决方案对,而拟议的误差则被表述为解决方案对等定义的构成关系错误。这种误差估计器提供了神经网络离散全球误差的上层界限。在示范性实例中研究了绑定属性以及物理知情神经网络解决方案的无症状行为。