PINNsによる固体力学解析の精度向上に関する研究

抄録

For physics-informed neural networks (PINNs)-based method for solid mechanics problems, deep energy method (DEM) has been proposed by Samaniego et al. Many PINN-based methods, including DEM, need a derivative operator in the definition of the loss function, and in most cases the derivative is obtained using automatic differentiation (AD) of the neural network model. AD is computed pointwise in the computational domain, eliminating the element-based discretization of the computational domain that is typically required in finite element methods (FEM) and allowing DEM for meshless simulations. However, the pointwise AD has the disadvantage of not being able to account for sharp gradients in physical quantities that occur between points. This may destabilize the DEM framework as it cannot detect steep strain gradients between the points. To address this issue, this paper introduces a gradient calculation method based on the shape functions of Lagrange finite elements and Gaussian quadrature within the DEM framework, replacing AD and the Monte Carlo method. The accuracy of the analysis results using this proposed DEM scheme is then examined.