  An efficient and expressive wavefunction ansatz is key to scalable solutions
for complex many-body electronic structures. While Slater determinants are
predominantly used for constructing antisymmetric electronic wavefunction
ans\"{a}tze, this construction can result in limited expressiveness when the
targeted wavefunction is highly complex. In this work, we introduce Waveflow,
an innovative framework for learning many-body fermionic wavefunctions using
boundary-conditioned normalizing flows. Instead of relying on Slater
determinants, Waveflow imposes antisymmetry by defining the fundamental domain
of the wavefunction and applying necessary boundary conditions. A key challenge
in using normalizing flows for this purpose is addressing the topological
mismatch between the prior and target distributions. We propose using O-spline
priors and I-spline bijections to handle this mismatch, which allows for
flexibility in the node number of the distribution while automatically
maintaining its square-normalization property. We apply Waveflow to a
one-dimensional many-electron system, where we variationally minimize the
system's energy using variational quantum Monte Carlo (VQMC). Our experiments
demonstrate that Waveflow can effectively resolve topological mismatches and
faithfully learn the ground-state wavefunction.
