# Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles

arXiv: https://arxiv.org/abs/2305.01754 · HTML: https://mlsanity.com/paper/2305.01754/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 80 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 20 of 20)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [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)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Gradients as a Measure of Uncertainty in Neural Networks](https://mlsanity.com/paper/2008.08030/) (2020)
- [Classification Uncertainty of Deep Neural Networks Based on Gradient Information](https://mlsanity.com/paper/1805.08440/) (2018)
- [Differentiable Molecular Simulations for Control and Learning](https://mlsanity.com/paper/2003.00868/) (2020)
- [Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks](https://mlsanity.com/paper/2101.11588/) (2021)
- [Generative Models for Automatic Chemical Design](https://mlsanity.com/paper/1907.01632/) (2019)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Materials Property Prediction with Uncertainty Quantification: A Benchmark Study](https://mlsanity.com/paper/2211.02235/) (2022)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [Gradient conjugate priors and multi-layer neural networks](https://mlsanity.com/paper/1802.02643/) (2018)

## Built on by (most cited first, 30 of 30)

- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Uncertainty Quantification Metrics for Deep Regression](https://mlsanity.com/paper/2405.04278/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Accurate machine learning force fields via experimental and simulation data fusion](https://mlsanity.com/paper/2308.09142/) (2023)
- [Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory](https://mlsanity.com/paper/2404.12367/) (2024)
- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [Machine-learning-accelerated simulations to enable automatic surface reconstruction](https://mlsanity.com/paper/2305.07251/) (2023)
- [BLIPs: Bayesian Learned Interatomic Potentials](https://mlsanity.com/paper/2508.14022/) (2025)
- [LTAU-FF: Loss Trajectory Analysis for Uncertainty in Atomistic Force Fields](https://mlsanity.com/paper/2402.00853/) (2024)
- [Outlier-Detection for Reactive Machine Learned Potential Energy Surfaces](https://mlsanity.com/paper/2402.17686/) (2024)
- [Are you sure? Analysing Uncertainty Quantification Approaches for Real-world Speech Emotion Recognition](https://mlsanity.com/paper/2407.01143/) (2024)
- [Knowing when to trust machine-learned interatomic potentials](https://mlsanity.com/paper/2605.00640/) (2026)
- [Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs](https://mlsanity.com/paper/2605.03964/) (2026)
- [Enhanced sampling of robust molecular datasets with uncertainty-based collective variables](https://mlsanity.com/paper/2402.03753/) (2024)
- [Neural Network Prediction of Strong Lensing Systems with Domain Adaptation and Uncertainty Quantification](https://mlsanity.com/paper/2411.03334/) (2024)
- [Physics-Based Hybrid Machine Learning for Critical Heat Flux Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2502.19357/) (2025)
- [Dataset Clustering for Improved Offline Policy Learning](https://mlsanity.com/paper/2402.09550/) (2024)
- [Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions](https://mlsanity.com/paper/2503.12354/) (2025)
- [Accelerating and enhancing thermodynamic simulations of electrochemical interfaces](https://mlsanity.com/paper/2503.17870/) (2025)
- [Constraint-Aware Neurosymbolic Uncertainty Quantification with Bayesian Deep Learning for Scientific Discovery](https://mlsanity.com/paper/2601.12442/) (2026)
- [Flowing with Confidence](https://mlsanity.com/paper/2605.18472/) (2026)
- [Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows](https://mlsanity.com/paper/2311.00060/) (2023)
- [Ensemble Learning of Machine Learning Force Fields](https://mlsanity.com/paper/2403.17507/) (2024)
- [A Framework for Uncertainty Quantification Based on Nearest Neighbors Across Layers](https://mlsanity.com/paper/2506.19895/) (2025)
- [Equivariant Evidential Deep Learning for Interatomic Potentials](https://mlsanity.com/paper/2602.10419/) (2026)
- [Uncertainty-Calibrated Diffusion for Reliable 3D Molecular Graph Generation](https://mlsanity.com/paper/2606.01595/) (2026)
- [ElemeNet: Multiscale Molecular Machine Learning with Uncertainty Quantification Across the Periodic Table](https://mlsanity.com/paper/2606.30961/) (2026)
- [Full-data accuracy with fewer labels for training and fine-tuning machine-learning force fields](https://mlsanity.com/paper/2607.14486/) (2026)
- [AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials](https://mlsanity.com/paper/2609.00488/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)

## Abstract (arXiv)

Neural networks (NNs) often assign high confidence to their predictions, even for points far out-of-distribution, making uncertainty quantification (UQ) a challenge. When they are employed to model interatomic potentials in materials systems, this problem leads to unphysical structures that disrupt simulations, or to biased statistics and dynamics that do not reflect the true physics. Differentiable UQ techniques can find new informative data and drive active learning loops for robust potentials. However, a variety of UQ techniques, including newly developed ones, exist for atomistic simulations and there are no clear guidelines for which are most effective or suitable for a given case. In this work, we examine multiple UQ schemes for improving the robustness of NN interatomic potentials (NNIPs) through active learning. In particular, we compare incumbent ensemble-based methods against strategies that use single, deterministic NNs: mean-variance estimation, deep evidential regression, and Gaussian mixture models. We explore three datasets ranging from in-domain interpolative learning to more extrapolative out-of-domain generalization challenges: rMD17, ammonia inversion, and bulk silica glass. Performance is measured across multiple metrics relating model error to uncertainty. Our experiments show that none of the methods consistently outperformed each other across the various metrics. Ensembling remained better at generalization and for NNIP robustness; MVE only proved effective for in-domain interpolation, while GMM was better out-of-domain; and evidential regression, despite its promise, was not the preferable alternative in any of the cases. More broadly, cost-effective, single deterministic models cannot yet consistently match or outperform ensembling for uncertainty quantification in NNIPs.