  Scientific machine learning and the advent of the Physics-Informed Neural
Network (PINN) show considerable potential in their capacity to identify
solutions to complex differential equations. Over the past two years, much work
has gone into the development of PINNs capable of solving the gravity field
modeling problem -- i.e.\ learning a differentiable form of the gravitational
potential from position and acceleration estimates. While the past PINN gravity
models (PINN-GMs) have demonstrated advantages in model compactness, robustness
to noise, and sample efficiency; there remain key modeling challenges which
this paper aims to address. Specifically, this paper introduces the third
generation of the Physics-Informed Neural Network Gravity Model (PINN-GM-III)
which solves the problems of extrapolation error, bias towards low-altitude
samples, numerical instability at high-altitudes, and compliant boundary
conditions through numerous modifications to the model's design. The
PINN-GM-III is tested by modeling a known heterogeneous density asteroid, and
its performance is evaluated using seven core metrics which showcases its
strengths against its predecessors and other analytic and numerical gravity
models.
