Machine Learning a Molecular Hamiltonian for Predicting Electron Dynamics
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We develop a mathematical method to learn a molecular Hamiltonian from matrix-valued time series of the electron density. As we demonstrate for each of three small molecules, the resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1000 time steps beyond the training data. As a more rigorous test, we use the learned Hamiltonians to simulate electron dynamics in the presence of an applied electric field, extrapolating to a problem that is beyond the field-free training data. The resulting electron dynamics predicted by our learned Hamiltonian are in close quantitative agreement with the ground truth. Our method relies on combining a reduced-dimensional, linear statistical model of the Hamiltonian with a time-discretization of the quantum Liouville equation. Ultimately, our model can be trained without recourse to numerous, CPU-intensive optimization steps. For all three molecules and both field-free and field-on problems, we quantify training and propagation errors, highlighting areas for future development.
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