# Uncertainty Estimation for Molecules: Desiderata and Methods

arXiv: https://arxiv.org/abs/2306.14916 · HTML: https://mlsanity.com/paper/2306.14916/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 86 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 30 of 51)

- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Hyperparameter Ensembles for Robustness and Uncertainty Quantification](https://mlsanity.com/paper/2006.13570/) (2020)
- [Confidence-Aware Learning for Deep Neural Networks](https://mlsanity.com/paper/2007.01458/) (2020)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)

## Built on by (most cited first, 11 of 11)

- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [LTAU-FF: Loss Trajectory Analysis for Uncertainty in Atomistic Force Fields](https://mlsanity.com/paper/2402.00853/) (2024)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [AUGUR, A flexible and efficient optimization algorithm for identification of optimal adsorption sites](https://mlsanity.com/paper/2409.16204/) (2024)
- [On Equivariant Model Selection through the Lens of Uncertainty](https://mlsanity.com/paper/2506.18629/) (2025)
- [Two Birds with One Stone: Enhancing Uncertainty Quantification and Interpretability with Graph Functional Neural Process](https://mlsanity.com/paper/2508.17097/) (2025)
- [Equivariant Evidential Deep Learning for Interatomic Potentials](https://mlsanity.com/paper/2602.10419/) (2026)
- [VINCENT: Validated Interaction Network for Cross-drug Explanation of Therapeutics](https://mlsanity.com/paper/2608.25841/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are promising surrogates for quantum mechanical calculations as they establish unprecedented low errors on collections of molecular dynamics (MD) trajectories. Thanks to their fast inference times they promise to accelerate computational chemistry applications. Unfortunately, despite low in-distribution (ID) errors, such GNNs might be horribly wrong for out-of-distribution (OOD) samples. Uncertainty estimation (UE) may aid in such situations by communicating the model's certainty about its prediction. Here, we take a closer look at the problem and identify six key desiderata for UE in molecular force fields, three 'physics-informed' and three 'application-focused' ones. To overview the field, we survey existing methods from the field of UE and analyze how they fit to the set desiderata. By our analysis, we conclude that none of the previous works satisfies all criteria. To fill this gap, we propose Localized Neural Kernel (LNK) a Gaussian Process (GP)-based extension to existing GNNs satisfying the desiderata. In our extensive experimental evaluation, we test four different UE with three different backbones and two datasets. In out-of-equilibrium detection, we find LNK yielding up to 2.5 and 2.1 times lower errors in terms of AUC-ROC score than dropout or evidential regression-based methods while maintaining high predictive performance.