  Molecular docking is critical to structure-based virtual screening, yet the
throughput of such workflows is limited by the expensive optimization of
scoring functions involved in most docking algorithms. We explore how machine
learning can accelerate this process by learning a scoring function with a
functional form that allows for more rapid optimization. Specifically, we
define the scoring function to be the cross-correlation of multi-channel ligand
and protein scalar fields parameterized by equivariant graph neural networks,
enabling rapid optimization over rigid-body degrees of freedom with fast
Fourier transforms. The runtime of our approach can be amortized at several
levels of abstraction, and is particularly favorable for virtual screening
settings with a common binding pocket. We benchmark our scoring functions on
two simplified docking-related tasks: decoy pose scoring and rigid conformer
docking. Our method attains similar but faster performance on crystal
structures compared to the widely-used Vina and Gnina scoring functions, and is
more robust on computationally predicted structures. Code is available at
https://github.com/bjing2016/scalar-fields.
