# Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System

arXiv: https://arxiv.org/abs/2112.07067 · HTML: https://mlsanity.com/paper/2112.07067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 14 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more](https://mlsanity.com/paper/1503.04021/) (2015)
- [Investigation of optimal control problems governed by a time-dependent Kohn-Sham model](https://mlsanity.com/paper/1701.02679/) (2017)

## Built on by (most cited first, 1 of 1)

- [Scalable learning of potentials to predict time-dependent Hartree-Fock dynamics](https://mlsanity.com/paper/2408.04765/) (2024)

## Abstract (arXiv)

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 Schr"odinger 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.