# Scalable learning of potentials to predict time-dependent Hartree-Fock dynamics

arXiv: https://arxiv.org/abs/2408.04765 · HTML: https://mlsanity.com/paper/2408.04765/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 8 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [Atomistic structure learning](https://mlsanity.com/paper/1902.10501/) (2019)
- [Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry](https://mlsanity.com/paper/2103.17233/) (2021)
- [Learning nonlinear integral operators via Recurrent Neural Networks and its application in solving Integro-Differential Equations](https://mlsanity.com/paper/2310.09434/) (2023)
- [Machine Learning a Molecular Hamiltonian for Predicting Electron Dynamics](https://mlsanity.com/paper/2007.09814/) (2020)
- [Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism](https://mlsanity.com/paper/2211.07482/) (2022)
- [Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System](https://mlsanity.com/paper/2112.07067/) (2021)
- [Incorporating Memory into Propagation of 1-Electron Reduced Density Matrices](https://mlsanity.com/paper/2403.15596/) (2024)

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

- [Machine Learning Time Propagators for Time-Dependent Density Functional Theory Simulations](https://mlsanity.com/paper/2508.16554/) (2025)

## Abstract (arXiv)

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.