论文标题
找到与欧几里得神经网络的对称破坏顺序参数
Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks
论文作者
论文摘要
居里的原则指出，“当效果显示某些不对称性时，必须在引起它们的原因中找到这种不对称性”。我们证明，对称性模棱两可的神经网络坚持居里的原则，可用于将许多与对称性的科学问题阐明为简单的优化问题。我们通过数学上证明这些属性，并通过训练欧几里得对称性的神经网络以数值方式证明它们，以学习对称性破坏的输入，以将正方形变形为矩形并在钙钛矿中产生八面的倾斜模式。
Curie's principle states that "when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them". We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many symmetry-relevant scientific questions into simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry-breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites.
