  Structural monitoring for complex built environments often suffers from
mismatch between design, laboratory testing, and actual built parameters.
Additionally, real-world structural identification problems encounter many
challenges. For example, the lack of accurate baseline models, high
dimensionality, and complex multivariate partial differential equations (PDEs)
pose significant difficulties in training and learning conventional data-driven
algorithms. This paper explores a new framework, dubbed NeuralSI, for
structural identification by augmenting PDEs that govern structural dynamics
with neural networks. Our approach seeks to estimate nonlinear parameters from
governing equations. We consider the vibration of nonlinear beams with two
unknown parameters, one that represents geometric and material variations, and
another that captures energy losses in the system mainly through damping. The
data for parameter estimation is obtained from a limited set of measurements,
which is conducive to applications in structural health monitoring where the
exact state of an existing structure is typically unknown and only a limited
amount of data samples can be collected in the field. The trained model can
also be extrapolated under both standard and extreme conditions using the
identified structural parameters. We compare with pure data-driven Neural
Networks and other classical Physics-Informed Neural Networks (PINNs). Our
approach reduces both interpolation and extrapolation errors in displacement
distribution by two to five orders of magnitude over the baselines. Code is
available at https://github.com/human-analysis/neural-structural-identification
