A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing that this method has a significantly higher convergence rate and accuracy than the vanilla physics-informed neural networks (PINN) and even SPINN based on a system of partial differential equations (PDEs). In addition, using the SPINN in the framework of DEM approach it is possible to solve problems of the linear theory of elasticity on complex geometries, which is unachievable with the help of PINNs in frames of partial differential equations. Considered problems are very close to the industrial problems in terms of geometry, loading, and material parameters.

翻译：提出了一种结合可分离物理信息神经网络（SPINN）与深度能量法（DEM）求解弹性问题的方法。针对多个问题的数值实验表明，该方法在收敛速度和精度上显著优于普通物理信息神经网络（PINN），甚至优于基于偏微分方程（PDE）系统的SPINN。此外，利用DEM框架下的SPINN，可以解决复杂几何形状上的线弹性理论问题，这是基于偏微分方程的PINN所无法实现的。所考虑的问题在几何形状、加载条件和材料参数等方面与工业实际问题非常接近。