标题： 评论“准常数SOAP和ACSF指纹流形及由此导致的机器学习四体相互作用失败” 显示英文标题

标题： Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions"

摘要： 最近由Parsaeifard和Goedecker发现的"准常数"SOAP和ACSF指纹流形是存在简并配置对的直接结果，这是所有低体阶原子密度相关分子结构表示的一个已知缺陷。 与严格奇异的配置相反——我们证明这些配置只能出现在有限的离散集合中——连续的"准常数"流形对原子位移表现出低但非零的敏感性。 因此，即使靠近精确奇点的数值不稳定性会影响这些模型的准确性和可转移性，具体程度取决于实现的数值细节，仍然可以在流形上构建高阶相互作用的插值机器学习模型。 显示英文摘要

摘要： The "quasi-constant" SOAP and ACSF fingerprint manifolds recently discovered by Parsaeifard and Goedecker are a direct consequence of the presence of degenerate pairs of configurations, a known shortcoming of all low-body-order atom-density correlation representations of molecular structures. Contrary to the configurations that are rigorously singular -- that we demonstrate can only occur in finite, discrete sets -- the continuous "quasi-constant" manifolds exhibit low, but non-zero, sensitivity to atomic displacements. Thus, it is possible to build interpolative machine-learning models of high-order interactions along the manifold, even though the numerical instabilities associated with proximity to the exact singularities affect the accuracy and transferability of such models, to an extent that depends on numerical details of the implementation.