# Fast Uncertainty Estimates in Deep Learning Interatomic Potentials

arXiv: https://arxiv.org/abs/2211.09866 · HTML: https://mlsanity.com/paper/2211.09866/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 17 Nov 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation](https://mlsanity.com/paper/1810.11890/) (2018)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [Committee neural network potentials control generalization errors and enable active learning](https://mlsanity.com/paper/2006.01541/) (2020)
- [Fast Neural Network Approach for Direct Covariant Forces Prediction in Complex Multi-Element Extended Systems](https://mlsanity.com/paper/1905.02791/) (2019)

## Built on by (most cited first, 22 of 22)

- [Matbench Discovery -- A framework to evaluate machine learning crystal stability predictions](https://mlsanity.com/paper/2308.14920/) (2023)
- [Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size](https://mlsanity.com/paper/2304.10061/) (2023)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials](https://mlsanity.com/paper/2312.01416/) (2023)
- [Accurate machine learning force fields via experimental and simulation data fusion](https://mlsanity.com/paper/2308.09142/) (2023)
- [Transfer learning for chemically accurate interatomic neural network potentials](https://mlsanity.com/paper/2212.03916/) (2022)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory](https://mlsanity.com/paper/2404.12367/) (2024)
- [Learning charges and long-range interactions from energies and forces](https://mlsanity.com/paper/2412.15455/) (2024)
- [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)
- [Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs](https://mlsanity.com/paper/2605.03964/) (2026)
- [Band-gap regression with architecture-optimized message-passing neural networks](https://mlsanity.com/paper/2309.06348/) (2023)
- [Enhanced sampling of robust molecular datasets with uncertainty-based collective variables](https://mlsanity.com/paper/2402.03753/) (2024)
- [LFaB: Low fidelity as Bias for Active Learning in the chemical configuration space](https://mlsanity.com/paper/2508.15577/) (2025)
- [Accelerating the Training and Improving the Reliability of Machine-Learned Interatomic Potentials for Strongly Anharmonic Materials through Active Learning](https://mlsanity.com/paper/2409.11808/) (2024)
- [Evaluation of uncertainty estimations for Gaussian process regression based machine learning interatomic potentials](https://mlsanity.com/paper/2410.20398/) (2024)
- [Accelerating and enhancing thermodynamic simulations of electrochemical interfaces](https://mlsanity.com/paper/2503.17870/) (2025)
- [A Systematic Survey and Benchmark of Deep Learning for Molecular Property Prediction in the Foundation Model Era](https://mlsanity.com/paper/2604.16586/) (2026)
- [Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows](https://mlsanity.com/paper/2311.00060/) (2023)
- [Comparing the latent features of universal machine-learning interatomic potentials](https://mlsanity.com/paper/2512.05717/) (2025)
- [AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials](https://mlsanity.com/paper/2609.00488/) (2026)

## Abstract (arXiv)

Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and materials properties. A common short-coming shared by current approaches, however, is that neural networks only give point estimates of their predictions and do not come with predictive uncertainties associated with these estimates. Existing uncertainty quantification efforts have primarily leveraged the standard deviation of predictions across an ensemble of independently trained neural networks. This incurs a large computational overhead in both training and prediction that often results in order-of-magnitude more expensive predictions. Here, we propose a method to estimate the predictive uncertainty based on a single neural network without the need for an ensemble. This allows us to obtain uncertainty estimates with virtually no additional computational overhead over standard training and inference. We demonstrate that the quality of the uncertainty estimates matches those obtained from deep ensembles. We further examine the uncertainty estimates of our methods and deep ensembles across the configuration space of our test system and compare the uncertainties to the potential energy surface. Finally, we study the efficacy of the method in an active learning setting and find the results to match an ensemble-based strategy at order-of-magnitude reduced computational cost.