Crystal material representation is the foundation of crystal material
research. Existing works consider crystal molecules as graph data with
different representation methods and leverage the advantages of techniques in
graph learning. A reasonable crystal representation method should capture the
local and global information. However, existing methods only consider the local
information of crystal molecules by modeling the bond distance and bond angle
of first-order neighbors of atoms, which leads to the issue that different
crystals will have the same representation. To solve this many-to-one issue, we
consider the global information by further considering dihedral angles, which
can guarantee that the proposed representation corresponds one-to-one with the
crystal material. We first propose a periodic complete representation and
calculation algorithm for infinite extended crystal materials. A theoretical
proof for the representation that satisfies the periodic completeness is
provided. Based on the proposed representation, we then propose a network for
predicting crystal material properties, PerCNet, with a specially designed
message passing mechanism. Extensive experiments are conducted on two
real-world material benchmark datasets. The PerCNet achieves the best
performance among baseline methods in terms of MAE. In addition, our results
demonstrate the importance of the periodic scheme and completeness for crystal
representation learning.

现有的晶体材料表示方法只考虑晶体分子的局部信息，通过考虑二面角进一步考虑全局信息后，我们首先提出了周期完备表示和计算算法，进而提出了一种特别设计的消息传递机制的网络 PerCNet 进行晶体材料性质预测。在实验证明了周期方案和完备性对晶体表示学习的重要性。

PerCNet: 周期完全表示与晶格

PerCNet: Periodic Complete Representation for Crystal Graphs

In the bioinformatics field, there has been a growing interest in modelling
dihedral angles of amino acids by viewing them as data on the torus. This has
motivated, over the past years, new proposals of distributions on the bivariate
torus. The main drawback of most of these models is that the related densities
are (pointwise) symmetric, despite the fact that the data usually present
asymmetric patterns. This motivates the need to find a new way of constructing
asymmetric toroidal distributions starting from a symmetric distribution. We
tackle this problem in this paper by introducing the sine-skewed toroidal
distributions. The general properties of the new models are derived. Based on
the initial symmetric model, explicit expressions for the shape parameters are
obtained, a simple algorithm for generating random numbers is provided, and
asymptotic results for the maximum likelihood estimators are established. An
important feature of our construction is that no normalizing constant needs to
be calculated, leading to more flexible distributions without increasing the
complexity of the models. The benefit of employing these new sine-skewed
distributions is shown on the basis of protein data, where, in general, the new
models outperform their symmetric antecedents.

本文提出了用正弦扭曲函数构造非对称环面分布的新方法，通过在蛋白数据方面表现出更好的效果，验证了这种方法的有效性。