A Three-Head Hamiltonian-consistent neural network for nonadiabatic time-dependent density functional theory dynamics

Abstract The exact exchange-correlation potential v xc in time-dependent density functional theory is a causal functional of the full density history, a dependence that widely used adiabatic approximations discard. We ask whether this history dependence can be approximated by a learnable finite-dimensional memory state while retaining a Hamiltonian-consistent description of the Kohn–Sham phase-space dynamics. To this end, we propose a Three-Head neural architecture consisting of a Hamiltonian dynamics head that induces a symplectic vector field from a parameterized scalar energy, a direct vector field head that supplies a flexible correction pathway, and a memory XC potential head that reconstructs v xc from density history through a recurrent memory module with cross-window carry. We evaluate the model on two physically distinct benchmarks. On the one-dimensional two-electron electron–hydrogen scattering model, it attains the lowest density reconstruction error among all baselines over the full propagation window, by the largest margin during the pre-collision approach phase, and is the only model that recovers the peak-and-step structure of v xc in the subsequent strongly nonadiabatic scattering window. On a one-dimensional helium Rabi oscillation model under strong-field driving, it reduces the correlation-potential reconstruction error by roughly an order of magnitude relative to all adiabatic baselines at every driven phase of both the Rabi and optical cycles, including the adiabatically exact ground-state limit, which shows that the residual error along the adiabatic axis is controlled by the missing density history rather than by the accuracy of the time-local map. Ablation studies show that structured dynamics and memory-based potential learning are mutually supportive rather than separable.