# Ensemble Learning of Machine Learning Force Fields

arXiv: https://arxiv.org/abs/2403.17507 · HTML: https://mlsanity.com/paper/2403.17507/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 62 references that are in the map.
- First posted on arXiv 26 Mar 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [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)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://mlsanity.com/paper/2103.01436/) (2021)
- [TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentials](https://mlsanity.com/paper/2306.06482/) (2023)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Committee neural network potentials control generalization errors and enable active learning](https://mlsanity.com/paper/2006.01541/) (2020)
- [Ensemble Learning of Coarse-Grained Molecular Dynamics Force Fields with a Kernel Approach](https://mlsanity.com/paper/2005.01851/) (2020)

## Abstract (arXiv)

Machine learning force fields (MLFFs) are a promising approach to balance the accuracy of quantum mechanics with the efficiency of classical potentials, yet selecting an optimal model amid increasingly diverse architectures that delivers reliable force predictions and stable simulations remains a core pratical challenge. Here we introduce EL-MLFFs, an ensemble learning framework that uses a stacking methodology to integrate predictions from diverse base MLFFs. Our approach constructs a graph representation where a graph neural network (GNN) acts as a meta-model to refine the initial force predictions. We present two meta-model architectures: a computationally efficient direct fitting model and a physically-principled conservative model that ensures energy conservation. The framework is evaluated on a diverse range of systems, including single molecules (methane), surface chemistry (methanol/Cu(100)), molecular dynamics benchmarks (MD17), and the MatPES materials dataset. Results show that EL-MLFFs improves predictive accuracy across these domains. For molecular systems, it reduces force errors and improves the simulation stability compared to base models. For materials, the method yields lower formation energy errors on the WBM test set. The EL- MLFFs framework offers a systematic approach to address challenges of model selection and the accuracy-stability trade-off in molecular and materials simulations.