  In this work, we propose a linear machine learning force matching approach
that can directly extract pair atomic interactions from ab initio calculations
in amorphous structures. The local feature representation is specifically
chosen to make the linear weights a force field as a force/potential function
of the atom pair distance. Consequently, this set of functions is the closest
representation of the ab initio forces given the two-body approximation and
finite scanning in the configurational space. We validate this approach in
amorphous silica. Potentials in the new force field (consisting of tabulated
Si-Si, Si-O, and O-O potentials) are significantly softer than existing
potentials that are commonly used for silica, even though all of them produce
the tetrahedral network structure and roughly similar glass properties. This
suggests that those commonly used classical force fields do not offer
fundamentally accurate representations of the atomic interaction in silica. The
new force field furthermore produces a lower glass transition temperature
($T_g\sim$1800 K) and a positive liquid thermal expansion coefficient,
suggesting the extraordinarily high $T_g$ and negative liquid thermal expansion
of simulated silica could be artifacts of previously developed classical
potentials. Overall, the proposed approach provides a fundamental yet intuitive
way to evaluate two-body potentials against ab initio calculations, thereby
offering an efficient way to guide the development of classical force fields.
