  Recent advances in machine learning have facilitated numerically accurate
solution of the electronic Schr\"{o}dinger equation (SE) by integrating various
neural network (NN)-based wavefunction ansatzes with variational Monte Carlo
methods. Nevertheless, such NN-based methods are all based on the
Born-Oppenheimer approximation (BOA) and require computationally expensive
training for each nuclear configuration. In this work, we propose a novel NN
architecture, Schr\"{o}dingerNet, to solve the full electronic-nuclear SE by
defining a loss function designed to equalize local energies across the system.
This approach is based on a rotationally equivariant total wavefunction ansatz
that includes both nuclear and electronic coordinates. This strategy not only
allows for the efficient and accurate generation of a continuous potential
energy surface at any geometry within the well-sampled nuclear configuration
space, but also incorporates non-BOA corrections through a single training
process. Comparison with benchmarks of atomic and molecular systems
demonstrates its accuracy and efficiency.
