Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System
This addresses a computational bottleneck in quantum chemistry for simulating electron dynamics, but it is incremental as it builds on existing methods in a low-dimensional setting.
The paper tackled the problem of learning correlation potentials for time-dependent Kohn-Sham systems in one dimension, showing that it is possible to learn values that match ground truth electron densities and demonstrating a model with memory that works for trajectories outside the training set.
We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schrödinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.