Statistical learning method for predicting density-matrix based electron dynamics
This work addresses electron dynamics prediction in molecular systems, but it is incremental as it extends a previous method with dimensionality reduction and regularization.
The authors tackled the problem of predicting electron dynamics from time-series density matrices by developing a statistical method that learns a molecular Hamiltonian, enabling solution of the Time-Dependent Hartree-Fock equation for field-free and field-on scenarios, with close quantitative agreement to ground truth observed.
We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce dimensionality, while also exploiting regularization techniques like ridge regression for addressing multicollinearity. With the learned Hamiltonian we can solve the Time-Dependent Hartree-Fock (TDHF) equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.