Machine-learning graph convolutional electronic propagators

We present a graph-based machine-learning framework for simulating the time evolution of electronic wavefunctions and densities in quantum systems. Inspired by parallels between time-dependent quantum propagators and spectral graph convolutions, we employ a recursive Chebyshev graph neural network architecture capable of learning the dynamics of electronic processes across a range of external potentials and Hamiltonians. Two model variants are introduced: one that evolves the full complex-valued wavefunction and the other that propagates only the electron density. Both models are trained on trajectory data generated from tight-binding Hamiltonians and a time-dependent electron-phonon coupled system. Our results demonstrate that wavefunction-based models achieve near-exact long-time propagation across static and dynamic regimes, while density-only models maintain strong performance using physics-informed loss functions, even in the absence of phase information. This work lays the foundation for coarse-grained, resolution-independent propagators for electronic dynamics and opens new pathways for scalable quantum simulations in complex molecular and condensed-phase systems.