# Graph Neural Network Interatomic Potential Ensembles with Calibrated Aleatoric and Epistemic Uncertainty on Energy and Forces

arXiv: https://arxiv.org/abs/2305.16325 · HTML: https://mlsanity.com/paper/2305.16325/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 10 of 10)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Less is more: sampling chemical space with active learning](https://mlsanity.com/paper/1801.09319/) (2018)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Committee neural network potentials control generalization errors and enable active learning](https://mlsanity.com/paper/2006.01541/) (2020)
- [Assigning Confidence to Molecular Property Prediction](https://mlsanity.com/paper/2102.11439/) (2021)
- [Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity concepts](https://mlsanity.com/paper/2303.07170/) (2023)

## Built on by (most cited first, 10 of 10)

- [Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivity](https://mlsanity.com/paper/2309.06240/) (2023)
- [MADE: Benchmark Environments for Closed-Loop Materials Discovery](https://mlsanity.com/paper/2601.20996/) (2026)
- [Stratification of uncertainties recalibrated by isotonic regression and its impact on calibration error statistics](https://mlsanity.com/paper/2306.05180/) (2023)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Credal Graph Neural Networks](https://mlsanity.com/paper/2512.02722/) (2025)
- [Negative impact of heavy-tailed uncertainty and error distributions on the reliability of calibration statistics for machine learning regression tasks](https://mlsanity.com/paper/2402.10043/) (2024)
- [Evaluation of uncertainty estimations for Gaussian process regression based machine learning interatomic potentials](https://mlsanity.com/paper/2410.20398/) (2024)
- [Coherent energy and force uncertainty in deep learning force fields](https://mlsanity.com/paper/2312.04174/) (2023)
- [Validation of ML-UQ calibration statistics using simulated reference values: a sensitivity analysis](https://mlsanity.com/paper/2403.00423/) (2024)
- [Online Surrogate Repair: Decoupling High-Fidelity Feedback from Search Length in Closed-Loop Discovery](https://mlsanity.com/paper/2609.07655/) (2026)

## Abstract (arXiv)

Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al.) and Transition1x (Schreiner et al.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.