  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.
