Physical Knowledge as Side Information for Neural Fermionic Wavefunctions

Neural wavefunctions provide a flexible approach to fermionic ground-state problems, but learning physically relevant correlations can remain difficult under finite optimization budgets. Existing methods often encode physical knowledge through architecture-specific modifications, making it hard to separate the value of the physical information from the way it is incorporated. We introduce a modular side-information architecture that makes fixed, Hamiltonian-derived physical computations available to a general fermionic neural wavefunction through trainable readers, while preserving its backbone architecture and determinant readout. The readers can act on particle features, pair communication, or orbitals, making the physical function, reader, and injection site explicit design choices. We evaluate this design on a three-dimensional attractive Fermi gas at infinite scattering length and a two-dimensional moiré electron system. In the Fermi gas, combining a two-body scattering-informed orbital correction with opposite-spin pair communication lowers the backbone energy by 1.82 ℏ²k_F²/m at 10,000 updates. With the reader and spectral modes fixed, the scattering relation lowers the energy relative to a matched constant relation. In the moiré system, four cross-attention readers using Hamiltonian-derived relations lower the energy by 0.12 to 0.19 E_h* at the same budget; density modes also help when read in every block. Across the two systems, the gain depends on the physical functions, their readers, and the injection sites.