# Multi-Fidelity Machine Learning for Excited State Energies of Molecules

arXiv: https://arxiv.org/abs/2305.11292 · HTML: https://mlsanity.com/paper/2305.11292/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 54 references that are in the map.
- First posted on arXiv 18 May 2023.

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

- [Machine learning for electronically excited states of molecules](https://mlsanity.com/paper/2007.05320/) (2020)
- [Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals](https://mlsanity.com/paper/1501.03854/) (2015)
- [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, 4 of 4)

- [Multitask methods for predicting molecular properties from heterogeneous data](https://mlsanity.com/paper/2401.17898/) (2024)
- [QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules](https://mlsanity.com/paper/2406.14149/) (2024)
- [Investigating Data Hierarchies in Multifidelity Machine Learning for Excitation Energies](https://mlsanity.com/paper/2410.11392/) (2024)
- [LFaB: Low fidelity as Bias for Active Learning in the chemical configuration space](https://mlsanity.com/paper/2508.15577/) (2025)

## Abstract (arXiv)

The accurate but fast calculation of molecular excited states is still a very challenging topic. For many applications, detailed knowledge of the energy funnel in larger molecular aggregates is of key importance requiring highly accurate excited state energies. To this end, machine learning techniques can be an extremely useful tool though the cost of generating highly accurate training datasets still remains a severe challenge. To overcome this hurdle, this work proposes the use of multi-fidelity machine learning where very little training data from high accuracies is combined with cheaper and less accurate data to achieve the accuracy of the costlier level. In the present study, the approach is employed to predict the first excited state energies for three molecules of increasing size, namely, benzene, naphthalene, and anthracene. The energies are trained and tested for conformations stemming from classical molecular dynamics simulations and from real-time density functional tight-binding calculations. It can be shown that the multi-fidelity machine learning model can achieve the same accuracy as a machine learning model built only on high cost training data while having a much lower computational effort to generate the data. The numerical gain observed in these benchmark test calculations was over a factor of 30 but certainly can be much higher for high accuracy data.