  We introduce an adaptive-weighted tree tensor network, for the study of
disordered and inhomogeneous quantum many-body systems. This ansatz is
assembled on the basis of the random couplings of the physical system with a
procedure that considers a tunable weight parameter to prevent completely
unbalanced trees. Using this approach, we compute the ground state of the
two-dimensional quantum Ising model in the presence of quenched random disorder
and frustration, with lattice size up to $32 \times 32$. We compare the results
with the ones obtained using the standard homogeneous tree tensor networks and
the completely self-assembled tree tensor networks, demonstrating a clear
improvement of numerical precision as a function of the weight parameter,
especially for large system sizes.
