  This paper introduces an innovative physics-informed deep learning framework
for metamodeling of nonlinear structural systems with scarce data. The basic
concept is to incorporate physics knowledge (e.g., laws of physics, scientific
principles) into deep long short-term memory (LSTM) networks, which boosts the
learning within a feasible solution space. The physics constraints are embedded
in the loss function to enforce the model training which can accurately capture
latent system nonlinearity even with very limited available training datasets.
Specifically for dynamic structures, physical laws of equation of motion, state
dependency and hysteretic constitutive relationship are considered to construct
the physics loss. In particular, two physics-informed multi-LSTM network
architectures are proposed for structural metamodeling. The satisfactory
performance of the proposed framework is successfully demonstrated through two
illustrative examples (e.g., nonlinear structures subjected to ground motion
excitation). It turns out that the embedded physics can alleviate overfitting
issues, reduce the need of big training datasets, and improve the robustness of
the trained model for more reliable prediction. As a result, the
physics-informed deep learning paradigm outperforms classical
non-physics-guided data-driven neural networks.
