Probing the effects of broken symmetries in machine learning

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 unconstrained models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We demonstrate that an unconstrained architecture can be trained to achieve a high degree of rotational invariance, testing the impacts of the small symmetry breaking 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 non-invariant behavior under rotations, 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.

This archive collect the input files, scripts, and data for the paper referenced below. In particular, it contains the trained MLIP for this work, the input files for simulations, the post-processing scripts and their outputs, as well as the plotting scripts and resulting figures. A detailed readme can be found below, and a more detailed one in each subfolder.

The data in this archive is mirrored at https://github.com/sirmarcel/eqt-archive, where issues can be raised and discussed.

对称性是物理学中最为核心的概念之一，因此它被广泛采纳为应用于物理科学领域机器学习模型的归纳偏置毫不奇怪。尤其是针对原子尺度物质性质的研究模型，这一现象尤为显著。无论是已建立的还是最前沿的方法，几乎无一例外，都是构建为对原子的平移、排列和旋转具有精确等变性的。引入对称性——尤其是旋转——对模型设计空间施加了约束，并暗示了更复杂的架构，这些架构通常也具有计算上的需求。有迹象表明，无约束的模型可以轻松地从数据中学习对称性，并且这样做甚至可能对模型的准确性产生益处。我们证明了无约束的架构可以被训练以实现高程度的旋转不变性，测试了在涉及气相、液相和固态水模拟的现实场景中，小对称性破缺的影响。我们特别关注那些可能受到旋转非不变行为——直接或间接——影响的物理可观测量，当模型在插值、整体状态下使用时，发现其后果微乎其微。即使在气相预测的外推情况下，模型也保持了极高的稳定性，尽管对称性伪影是明显的。我们还讨论了可以用来系统性地减少对称性破缺幅度的策略，并评估了它们对可观测量收敛的影响。

本存档收集了以下论文的输入文件、脚本和数据。特别是，它包含了本工作的训练好的MLIP，模拟的输入文件，后处理脚本及其输出，以及绘图脚本和生成的图像。详细的readme文件可以在下面找到，以及在每个子文件夹中都有更详细的说明。

本存档中的数据在https://github.com/sirmarcel/eqt-archive上进行了镜像，在那里可以提出和讨论问题。