准常数SOAP和ACSF指纹的流形以及由此导致的机器学习四体相互作用的失败
Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions
摘要：
原子指纹通常用于在机器学习和其他上下文中表征原子的局部环境。在这项工作中，我们研究了两个广泛使用的指纹，即原子位置的光滑重叠（SOAP）和原子中心对称函数（ACSF），在有限的原子位置的变化，并证明了存在的流形的准常数指纹。这些流形是通过以下准零特征值的灵敏度矩阵的特征向量的数值。ACSF和SOAP中这种流形的存在导致机器学习四体相互作用失败，例如标准力场中的扭转能量。重叠矩阵指纹由于其固有的多体特征而没有这样的流形。
英文摘要：
Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSF), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the sensitivity matrix with quasi-zero eigenvalues. The existence of such manifolds in ACSF and SOAP causes a failure to machine learn four-body interactions such as torsional energies that are part of standard force fields. No such manifolds can be found for the Overlap Matrix (OM) fingerprint due to its intrinsic many-body character.
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