# Self-consistent Validation for Machine Learning Electronic Structure

arXiv: https://arxiv.org/abs/2402.10186 · HTML: https://mlsanity.com/paper/2402.10186/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 7 of 7)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Eigenvalue and Generalized Eigenvalue Problems: Tutorial](https://mlsanity.com/paper/1903.11240/) (2019)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)
- [DeepDFT: Neural Message Passing Network for Accurate Charge Density Prediction](https://mlsanity.com/paper/2011.03346/) (2020)

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

- [Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models](https://mlsanity.com/paper/2406.03794/) (2024)
- [A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction](https://mlsanity.com/paper/2606.14498/) (2026)

## Abstract (arXiv)

Machine learning has emerged as a significant approach to efficiently tackle electronic structure problems. Despite its potential, there is less guarantee for the model to generalize to unseen data that hinders its application in real-world scenarios. To address this issue, a technique has been proposed to estimate the accuracy of the predictions. This method integrates machine learning with self-consistent field methods to achieve both low validation cost and interpret-ability. This, in turn, enables exploration of the model's ability with active learning and instills confidence in its integration into real-world studies.