  The experimental realization of Fermi-Hubbard tweezer arrays opens a new
stage for engineering fermionic matter, where programmable lattice geometries
and Hubbard model parameters are combined with single-site imaging. In order to
use these versatile experimental Fermi-Hubbard models as quantum simulators, it
is crucial to know the Hubbard parameters describing them. Here we develop
methods to calculate the Hubbard model parameters of arbitrary two-dimensional
lattice geometries: the tunneling $t$, on-site potential $V$, and interaction
$U$, for multiple bands and for both fermions and bosons. We show several
examples. One notable finding is that a finite array of equally strong and
separated individual tweezer potentials actually sums to give a non-periodic
total potential and thus spatially non-uniform Hubbard parameters. We
demonstrate procedures to find trap configurations that equalize these
parameters. More generally, these procedures solve the inverse problem of
calculating Hubbard parameters: given desired Hubbard parameters, find trap
configurations to realize them. These methods will be critical tools for using
tunnel-coupled tweezer arrays.
