  Data-driven models for predicting dynamic responses of linear and nonlinear
systems are of great importance due to their wide application from
probabilistic analysis to inverse problems such as system identification and
damage diagnosis. In this study, a physics-based recurrent neural network model
is designed that is able to learn the dynamics of linear and nonlinear multiple
degrees of freedom systems given a ground motion. The model is able to estimate
a complete set of responses, including displacement, velocity, acceleration,
and internal forces. Compared to the most advanced counterparts, this model
requires a smaller number of trainable variables while the accuracy of
predictions is higher for long trajectories. In addition, the architecture of
the recurrent block is inspired by differential equation solver algorithms and
it is expected that this approach yields more generalized solutions. In the
training phase, we propose multiple novel techniques to dramatically accelerate
the learning process using smaller datasets, such as hardsampling, utilization
of trajectory loss function, and implementation of a trust-region approach.
Numerical case studies are conducted to examine the strength of the network to
learn different nonlinear behaviors. It is shown that the network is able to
capture different nonlinear behaviors of dynamic systems with very high
accuracy and with no need for prior information or very large datasets.
