  Fast and accurate structural dynamics analysis is important for structural
design and damage assessment. Structural dynamics analysis leveraging machine
learning techniques has become a popular research focus in recent years.
Although the basic neural network provides an alternative approach for
structural dynamics analysis, the lack of physics law inside the neural network
limits the model accuracy and fidelity. In this paper, a new family of the
energy-conservation neural network is introduced, which respects the physical
laws. The neural network is explored from a fundamental
single-degree-of-freedom system to a complicated multiple-degrees-of-freedom
system. The damping force and external forces are also considered step by step.
To improve the parallelization of the algorithm, the derivatives of the
structural states are parameterized with the novel energy-conservation neural
network instead of specifying the discrete sequence of structural states. The
proposed model uses the system energy as the last layer of the neural network
and leverages the underlying automatic differentiation graph to incorporate the
system energy naturally, which ultimately improves the accuracy and long-term
stability of structures dynamics response calculation under an earthquake
impact. The trade-off between computation accuracy and speed is discussed. As a
case study, a 3-story building earthquake simulation is conducted with
realistic earthquake records.
