Nigam Jigyasa, Pozdnyakov Sergey, Ceriotti Michele
Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
J Chem Phys. 2020 Sep 28;153(12):121101. doi: 10.1063/5.0021116.
Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible N-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different order (generalizations of N-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically improvable, symmetry adapted representations for atomistic machine learning.
将原子构型映射到与原子位置相关的场（例如原子密度）的对称化N点关联，已成为一种优雅且有效的解决方案，可将结构表示为机器学习算法的输入。虽然已经很清楚低阶密度关联不能完整地表示原子环境，但可能的N体不变量数量呈指数增长，这使得设计简洁有效的表示变得困难。我们讨论了如何利用不同阶的等变特征（提供非真旋转对称性完整表示的N体不变量的推广）之间的递归关系来高效计算高阶项。结合在每个阶自动选择最具表现力的特征组合，这种方法提供了一个概念性和实用性的框架，用于为原子机器学习生成可系统改进的、适应对称性的表示。
