2024/08/08 by Harish S. Bhat, Bhat, Harish S., Prachi Gupta +3 · 2 citations
Physics and Astronomy · #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (stat.ML) #Spectroscopy and Quantum Chemical Studies #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2408.04765
openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a framework to learn the time-dependent Hartree-Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Though the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange-correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.