论文标题
通过机器学习的量子力学模拟插值的分子和材料的表示
Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning
论文作者
论文摘要
第一原理分子和材料的计算研究是物理，化学和材料科学的基石，但受到准确和精确模拟的成本的限制。在涉及许多模拟的设置中，机器学习可以通过参考模拟之间的插值来降低这些成本，通常是通过数量级来降低这些成本。这需要描述任何分子或材料并支持插值的表示。 我们使用基于多体函数，平均群体和张量产品的统一数学框架，全面审查和讨论当前表示及其之间的关系。对于选定的最先进表示形式，我们比较了有机分子，二元合金和Al-GA-IN曲二氧化物的能量预测，这些数值实验控制了用于数据分布，回归方法和高参数优化的数值实验。
Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry, and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, often by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We comprehensively review and discuss current representations and relations between them, using a unified mathematical framework based on many-body functions, group averaging, and tensor products. For selected state-of-the-art representations, we compare energy predictions for organic molecules, binary alloys, and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method, and hyper-parameter optimization.
