Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms. Incorporating symmetries -- rotations in particular -- constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that non-symmetric models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We put a model that obeys rotational invariance only approximately to the test, in realistic scenarios involving simulations of gas-phase, liquid, and solid water. We focus specifically on physical observables that are likely to be affected -- directly or indirectly -- by symmetry breaking, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables.

翻译：对称性是物理学中最核心的概念之一，因此它被广泛采纳为应用于物理科学的机器学习模型的归纳偏置也就不足为奇了。对于针对原子尺度物质性质的模型而言尤其如此。无论是已确立的方法还是最先进的方法，几乎无一例外，都被构建为对原子的平移、置换和旋转具有精确的等变性。融入对称性——尤其是旋转对称性——限制了模型的设计空间，并通常意味着更复杂且计算要求更高的架构。有迹象表明，非对称模型可以轻松地从数据中学习对称性，而且这样做甚至可能有利于模型的准确性。我们在涉及气相、液态和固态水模拟的现实场景中，对一个仅近似服从旋转不变性的模型进行了测试。我们特别关注那些可能直接或间接受对称性破缺影响的物理可观测量，发现当模型用于内插性的体相体系时，其影响微乎其微。即使对于外推性的气相预测，模型也保持非常稳定，尽管对称性伪影是明显的。我们还讨论了可用于系统性地减小对称性破缺发生时其影响幅度的策略，并评估了这些策略对可观测量收敛性的影响。