Equivariant Cellular Sheaves for Molecular Electronic Structure: Bridging Sheaf Cohomology and E(3)-Equivariant Hamiltonian Learning
Researchers propose modeling molecular single-particle Hamiltonians as Laplacians of cellular sheaves to improve E(3)-equivariant learning.
This paper bridges topological deep learning and molecular physics by demonstrating that molecular Hamiltonians, when expressed in a localized atomic-orbital basis, function as Laplacians on a regular cell complex. This structural insight provides a new framework for E(3)-equivariant Hamiltonian prediction, moving beyond standard message-passing networks.
