# Electronic excited states from physically-constrained machine learning

arXiv: https://arxiv.org/abs/2311.00844 · HTML: https://mlsanity.com/paper/2311.00844/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 76 references that are in the map.
- First posted on arXiv 1 Nov 2023.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian](https://mlsanity.com/paper/2306.04922/) (2023)
- [Machine learning for electronically excited states of molecules](https://mlsanity.com/paper/2007.05320/) (2020)
- [Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties](https://mlsanity.com/paper/2109.12083/) (2021)
- [Unified theory of atom-centered representations and message-passing machine-learning schemes](https://mlsanity.com/paper/2202.01566/) (2022)
- [Neural networks and kernel ridge regression for excited states dynamics of CH2NH2^+: From single-state to multi-state representations and multi-property machine learning models](https://mlsanity.com/paper/1912.08484/) (2019)

## Built on by (most cited first, 2 of 2)

- [Multi-task learning for molecular electronic structure approaching coupled-cluster accuracy](https://mlsanity.com/paper/2405.12229/) (2024)
- [Chemistry-Enhanced Diffusion-Based Framework for Small-to-Large Molecular Conformation Generation](https://mlsanity.com/paper/2511.12182/) (2025)

## Abstract (arXiv)

Data-driven techniques are increasingly used to replace electronic-structure calculations of matter. In this context, a relevant question is whether machine learning (ML) should be applied directly to predict the desired properties or be combined explicitly with physically-grounded operations. We present an example of an integrated modeling approach, in which a symmetry-adapted ML model of an effective Hamiltonian is trained to reproduce electronic excitations from a quantum-mechanical calculation. The resulting model can make predictions for molecules that are much larger and more complex than those that it is trained on, and allows for dramatic computational savings by indirectly targeting the outputs of well-converged calculations while using a parameterization corresponding to a minimal atom-centered basis. These results emphasize the merits of intertwining data-driven techniques with physical approximations, improving the transferability and interpretability of ML models without affecting their accuracy and computational efficiency, and providing a blueprint for developing ML-augmented electronic-structure methods.