# High Accuracy Uncertainty-Aware Interatomic Force Modeling with Equivariant Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2304.03694 · HTML: https://mlsanity.com/paper/2304.03694/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 5 Apr 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (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)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [Nudged elastic band calculations accelerated with Gaussian process regression](https://mlsanity.com/paper/1706.04606/) (2017)
- [Molecular Dynamics with Neural-Network Potentials](https://mlsanity.com/paper/1812.07676/) (2018)

## Built on by (most cited first, 2 of 2)

- [On-the-Fly Fine-Tuning of Foundational Neural Network Potentials: A Bayesian Neural Network Approach](https://mlsanity.com/paper/2507.13805/) (2025)
- [Equivariant Covariance Tensors: Guaranteed SPD Uncertainty for Tensor-Valued Geometric Learning](https://mlsanity.com/paper/2608.24386/) (2026)

## Abstract (arXiv)

Even though Bayesian neural networks offer a promising framework for modeling uncertainty, active learning and incorporating prior physical knowledge, few applications of them can be found in the context of interatomic force modeling. One of the main challenges in their application to learning interatomic forces is the lack of suitable Monte Carlo Markov chain sampling algorithms for the posterior density, as the commonly used algorithms do not converge in a practical amount of time for many of the state-of-the-art architectures. As a response to this challenge, we introduce a new Monte Carlo Markov chain sampling algorithm in this paper which can circumvent the problems of the existing sampling methods. In addition, we introduce a new stochastic neural network model based on the NequIP architecture and demonstrate that, when combined with our novel sampling algorithm, we obtain predictions with state-of-the-art accuracy as well as a good measure of uncertainty.