Deep Energy Method

The deep energy method is an alternative to the physics-informed neural networks (PINNs). Both approaches leverage the underlying physics to reduce the amount of data required. Instead of directly using the governing differential equations, the deep energy method minimizes the potential energy of the underlying physical system. This approach lowers the required order of derivatives and decreases the computational effort. Additionally, it is easier to handle singularities than with the PINNs. However, this approach cannot be used for the identification of differential equations. The method is illustrated with the same static bar example from Chap. 2, where the displacement is estimated.