  The goal of this paper is to provide a simple approach to perform local
sensitivity analysis using Physics-informed neural networks (PINN). The main
idea lies in adding a new term in the loss function that regularizes the
solution in a small neighborhood near the nominal value of the parameter of
interest. The added term represents the derivative of the loss function with
respect to the parameter of interest. The result of this modification is a
solution to the problem along with the derivative of the solution with respect
to the parameter of interest (the sensitivity). We call the new technique
SA-PNN which stands for sensitivity analysis in PINN. The effectiveness of the
technique is shown using four examples: the first one is a simple
one-dimensional advection-diffusion problem to show the methodology, the second
is a two-dimensional Poisson's problem with nine parameters of interest, and
the third and fourth examples are one and two-dimensional transient two-phase
flow in porous media problem.
