论文标题
高弹性和粘弹性的深度学习能量方法
A deep learning energy method for hyperelasticity and viscoelasticity
论文作者
论文摘要
合并了势能公式和深度学习，以求解局部微分方程，以管理超弹性和粘弹性材料中的变形。提出的深度能量法（DEM）是独立的，无环。它可以准确捕获三维（3D）机械响应，而无需通过经典数值方法（例如有限元方法）进行任何耗时的训练数据。一旦对模型进行了适当的训练，鉴于其空间坐标，几乎可以立即在物理领域的任何时刻获得响应。因此，深度能量方法可能是一种有希望的独立方法，用于求解描述材料或结构系统和其他物理现象的机械变形的部分微分方程。
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation by classical numerical methods such as the finite element method. Once the model is appropriately trained, the response can be attained almost instantly at any point in the physical domain, given its spatial coordinates. Therefore, the deep energy method is potentially a promising standalone method for solving partial differential equations describing the mechanical deformation of materials or structural systems and other physical phenomena.
