Machine learning force fields (MLFFs) have emerged as a promising approach to bridge the accuracy of quantum mechanical methods and the efficiency of classical force fields. However, the abundance of MLFF models and the challenge of accurately predicting atomic forces pose significant obstacles in their practical application. In this paper, we propose a novel ensemble learning framework, EL-MLFFs, which leverages the stacking method to integrate predictions from diverse MLFFs and enhance force prediction accuracy. By constructing a graph representation of molecular structures and employing a graph neural network (GNN) as the meta-model, EL-MLFFs effectively captures atomic interactions and refines force predictions. We evaluate our approach on two distinct datasets: methane molecules and methanol adsorbed on a Cu(100) surface. The results demonstrate that EL-MLFFs significantly improves force prediction accuracy compared to individual MLFFs, with the ensemble of all eight models yielding the best performance. Moreover, our ablation study highlights the crucial roles of the residual network and graph attention layers in the model's architecture. The EL-MLFFs framework offers a promising solution to the challenges of model selection and force prediction accuracy in MLFFs, paving the way for more reliable and efficient molecular simulations.

通过构建分子结构的图表示并利用图神经网络（GNN）作为元模型，EL-MLFFs有效地捕捉了原子间相互作用并优化了力预测，实验证明EL-MLFFs相对于独立的MLFFs显著提高了力预测准确性，最佳性能由所有八个模型组合得出。此外，剩余网络和图注意力层在模型的架构中起到了关键作用，EL-MLFFs框架为MLFF的模型选择和力预测准确性的挑战提供了一个有前景的解决方案，为更可靠高效的分子模拟铺平了道路。

EL-MLFFs: 集成学习的机器学习力场