# Calibrated Uncertainty for Molecular Property Prediction using Ensembles of Message Passing Neural Networks

arXiv: https://arxiv.org/abs/2107.06068 · HTML: https://mlsanity.com/paper/2107.06068/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 13 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials](https://mlsanity.com/paper/1806.03146/) (2018)
- [Assigning Confidence to Molecular Property Prediction](https://mlsanity.com/paper/2102.11439/) (2021)

## Built on by (most cited first, 21 of 21)

- [Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivity](https://mlsanity.com/paper/2309.06240/) (2023)
- [Graph Neural Networks in Modern AI-aided Drug Discovery](https://mlsanity.com/paper/2506.06915/) (2025)
- [MUBen: Benchmarking the Uncertainty of Molecular Representation Models](https://mlsanity.com/paper/2306.10060/) (2023)
- [Calibration and generalizability of probabilistic models on low-data chemical datasets with DIONYSUS](https://mlsanity.com/paper/2212.01574/) (2022)
- [On the role of Model Uncertainties in Bayesian Optimization](https://mlsanity.com/paper/2301.05983/) (2023)
- [Uncertainty Quantification for Molecular Property Predictions with Graph Neural Architecture Search](https://mlsanity.com/paper/2307.10438/) (2023)
- [Properties of the ENCE and other MAD-based calibration metrics](https://mlsanity.com/paper/2305.11905/) (2023)
- [Stratification of uncertainties recalibrated by isotonic regression and its impact on calibration error statistics](https://mlsanity.com/paper/2306.05180/) (2023)
- [MaterialsAtlas.org: A Materials Informatics Web App Platform for Materials Discovery and Survey of State-of-the-Art](https://mlsanity.com/paper/2109.04007/) (2021)
- [Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity concepts](https://mlsanity.com/paper/2303.07170/) (2023)
- [Can bin-wise scaling improve consistency and adaptivity of prediction uncertainty for machine learning regression ?](https://mlsanity.com/paper/2310.11978/) (2023)
- [LTAU-FF: Loss Trajectory Analysis for Uncertainty in Atomistic Force Fields](https://mlsanity.com/paper/2402.00853/) (2024)
- [Band-gap regression with architecture-optimized message-passing neural networks](https://mlsanity.com/paper/2309.06348/) (2023)
- [Advancements in Molecular Property Prediction: A Survey of Single and Multimodal Approaches](https://mlsanity.com/paper/2408.09461/) (2024)
- [Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?](https://mlsanity.com/paper/2605.22593/) (2026)
- [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)
- [Improving Counterfactual Truthfulness for Molecular Property Prediction through Uncertainty Quantification](https://mlsanity.com/paper/2504.02606/) (2025)
- [Coherent energy and force uncertainty in deep learning force fields](https://mlsanity.com/paper/2312.04174/) (2023)
- [AIRI: Predicting Retention Indices and their Uncertainties using Artificial Intelligence](https://mlsanity.com/paper/2401.01506/) (2024)
- [Validation of ML-UQ calibration statistics using simulated reference values: a sensitivity analysis](https://mlsanity.com/paper/2403.00423/) (2024)
- [Practical Deep Heteroskedastic Regression](https://mlsanity.com/paper/2603.01750/) (2026)

## Abstract (arXiv)

Data-driven methods based on machine learning have the potential to accelerate computational analysis of atomic structures. In this context, reliable uncertainty estimates are important for assessing confidence in predictions and enabling decision making. However, machine learning models can produce badly calibrated uncertainty estimates and it is therefore crucial to detect and handle uncertainty carefully. In this work we extend a message passing neural network designed specifically for predicting properties of molecules and materials with a calibrated probabilistic predictive distribution. The method presented in this paper differs from previous work by considering both aleatoric and epistemic uncertainty in a unified framework, and by recalibrating the predictive distribution on unseen data. Through computer experiments, we show that our approach results in accurate models for predicting molecular formation energies with well calibrated uncertainty in and out of the training data distribution on two public molecular benchmark datasets, QM9 and PC9. The proposed method provides a general framework for training and evaluating neural network ensemble models that are able to produce accurate predictions of properties of molecules with well calibrated uncertainty estimates.