  Physics-Informed Neural Networks (PINNs) have recently shown great promise as
a way of incorporating physics-based domain knowledge, including fundamental
governing equations, into neural network models for many complex engineering
systems. They have been particularly effective in the area of inverse problems,
where boundary conditions may be ill-defined, and data-absent scenarios, where
typical supervised learning approaches will fail. Here, we further explore the
use of this modeling methodology to surrogate modeling of a fluid dynamical
system, and demonstrate additional undiscussed and interesting advantages of
such a modeling methodology over conventional data-driven approaches: 1)
improving the model's predictive performance even with incomplete description
of the underlying physics; 2) improving the robustness of the model to noise in
the dataset; 3) reduced effort to convergence during optimization for a new,
previously unseen scenario by transfer optimization of a pre-existing model.
Hence, we noticed the inclusion of a physics-based regularization term can
substantially improve the equivalent data-driven surrogate model in many
substantive ways, including an order of magnitude improvement in test error
when the dataset is very noisy, and a 2-3x improvement when only partial
physics is included. In addition, we propose a novel transfer optimization
scheme for use in such surrogate modeling scenarios and demonstrate an
approximately 3x improvement in speed to convergence and an order of magnitude
improvement in predictive performance over conventional Xavier initialization
for training of new scenarios.
