[论文解读] Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction

Yuchao Lin, Keqiang Yan+4 more|arXiv (Cornell University)|Jun 12, 2023

Machine Learning in Materials Science被引用 10

一句话总结

PotNet 引入基于物理的原子间势以及完整的原子间势求和，通过基于 Ewald 的方法近似，整合到 GNN 中以在 Materials Project 和 JARVIS 基准上提高晶体属性预测的准确性。

ABSTRACT

We study property prediction for crystal materials. A crystal structure consists of a minimal unit cell that is repeated infinitely in 3D space. How to accurately represent such repetitive structures in machine learning models remains unresolved. Current methods construct graphs by establishing edges only between nearby nodes, thereby failing to faithfully capture infinite repeating patterns and distant interatomic interactions. In this work, we propose several innovations to overcome these limitations. First, we propose to model physics-principled interatomic potentials directly instead of only using distances as in many existing methods. These potentials include the Coulomb potential, London dispersion potential, and Pauli repulsion potential. Second, we model the complete set of potentials among all atoms, instead of only between nearby atoms as in existing methods. This is enabled by our approximations of infinite potential summations, where we extend the Ewald summation for several potential series approximations with provable error bounds. Finally, we propose to incorporate our computations of complete interatomic potentials into message passing neural networks for representation learning. We perform experiments on the JARVIS and Materials Project benchmarks for evaluation. Results show that the use of interatomic potentials and complete interatomic potentials leads to consistent performance improvements with reasonable computational costs. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS/tree/main/OpenMat/PotNet).

研究动机与目标

• 通过利用基于物理原理的原子间势，推动超越仅基于近邻相互作用图的晶体属性预测。
• 引入完整的原子间势求和，以捕捉无限重复单胞的相互作用。
• 将这些势整合到消息传递框架中，以学习晶体表征。
• 提供对于无限势求和的高效算法，具有可证明的误差界限。
• 在大型晶体基准测试（Materials Project、JARVIS）上展示性能提升。

提出的方法

• 直接建模原子间势（库仑力、伦敦色散、泡利排斥）作为边特征，而不仅仅依赖距离。
• 扩展为跨越所有周期重复的完整原子间势，使用具有可证明误差界限的无限和近似。
• 重写能量计算以对完整势进行求和，并将其嵌入到 GNN 的消息传递方案中。
• 使用基于 Ewald 的方法高效近似无限求和，将其拆分为快速收敛的实空间和傅里叶空间分量，并在适用处通过不完全贝塞尔函数表示。
• 将 PotNet 实现为一个三维 GNN，将无限势和 S(a,b) 视为边特征，并在每对 (a,b) 之间仅用一条边对所有单胞进行聚合。
• 在 Materials Project 和 JARVIS 上提供带有消融实验和计算指标的训练与评估细节。

Figure 1: Schematic illustrations of how complete interatomic interactions are captured in PotNet. Note that PotNet models 3D crystals while we have 2D illustration for simplicity. (a) An example crystal in which each unit cell contains two atoms $a$ and $b$ . In PotNet, the potentials between all p

实验结果

研究问题

• RQ1 基于物理原理的原子间势能是否能够超越基于距离的图，对晶体属性预测带来改进？
• RQ2 在控制误差界的前提下，如何高效近似无限的原子间势求和？
• RQ3 将完整的原子间势纳入 GNN 是否在标准晶体基准上提高预测准确性？

主要发现

方法	形成能（eV/原子）	带隙（eV）	体模量（log(GPa)）	剪切模量（log(GPa)）
CGCNN	0.031	0.292	0.047	0.077
SchNet	0.033	0.345	0.066	0.099
MEGNET	0.030	0.307	0.051	0.099
GATGNN	0.033	0.280	0.045	0.075
ALIGNN	0.0221	0.218	0.051	0.078
Matformer	0.0210	0.211	0.043	0.073
PotNet	0.0188	0.204	0.040	0.065

• PotNet 在 Materials Project 和 JARVIS 基准测试上持续提升相较强基线的预测性能。
• 使用完整的原子间势在能量和性质预测上优于仅使用半径的相互作用。
• 所提出的基于 Ewald 的求和提供快速、可证明有界的无限势求和近似，使可扩展训练成为可能。
• 相比最先进模型，PotNet 实现了更低的形成能预测误差以及具有竞争力或更优的带隙和模量预测。

Figure 2: The developed network architecture for PotNet. The notations used in this figure are defined as follows: $\sigma$ denotes the sigmoid function; $\|_{a}$ represents the concatenation operation along the dimension $a$ ; $\odot$ signifies the Hadamard product, or element-wise multiplication o