The conventional definition of hypergraph has two major issues: (1) there is
not a standard definition of directed hypergraph and (2) there is not a formal
definition of nested hypergraph. To resolve these issues, we propose a new
definition of hypergraph that unifies the concepts of undirected, directed and
nested hypergraphs, and that is uniform in using hyperedge as a single
construct for representing high-order correlations among things, i.e., nodes
and hyperedges. Specifically, we define a hyperedge to be a simple hyperedge, a
nesting hyperedge, or a directed hyperedge. With this new definition, a
hypergraph is nested if it has nesting hyperedge(s), and is directed if it has
directed hyperedge(s). Otherwise, a hypergraph is a simple hypergraph. The
uniformity and power of this new definition should facilitate the use of
hypergraph for representing (hierarchical) high-order correlations in general
and chemical systems in particular. Graph has been widely used as a
mathematical structure for machine learning on molecular structures and 3D
molecular geometries. However, graph has a major limitation: it can represent
only pairwise correlations between nodes. Hypergraph extends graph with
high-order correlations among nodes. This extension is significant or essential
for machine learning on chemical systems. For molecules, this is significant as
it allows the direct, explicit representation of multicenter bonds and
molecular substructures. For chemical reactions, this is essential since most
chemical reactions involve multiple participants. We propose the use of
chemical hypergraph, a multilevel hypergraph with simple, nesting and directed
hyperedges, as a single mathematical structure for representing chemical
systems. We apply the new definition of hypergraph to chemical hypergraph and,
as simplified versions, molecular hypergraph and chemical reaction hypergraph.

通过新定义的超图，将无向超图、有向超图和嵌套超图的概念统一起来，以超边作为高阶事物之间的关联的单一结构，方便地表示一般和化学系统中的高阶关联，尤其适用于化学系统的机器学习。

超图：一个统一且一致的定义及其在化学超图中的应用

Hypergraph: A Unified and Uniform Definition with Application to  Chemical Hypergraph

We present a method for the unsupervised segmentation of electron microscopy
images, which are powerful descriptors of materials and chemical systems.
Images are oversegmented into overlapping chips, and similarity graphs are
generated from embeddings extracted from a domain$\unicode{x2010}$pretrained
convolutional neural network (CNN). The Louvain method for community detection
is then applied to perform segmentation. The graph representation provides an
intuitive way of presenting the relationship between chips and communities. We
demonstrate our method to track irradiation$\unicode{x2010}$induced amorphous
fronts in thin films used for catalysis and electronics. This method has
potential for "on$\unicode{x2010}$the$\unicode{x2010}$fly" segmentation to
guide emerging automated electron microscopes.

使用无监督分割方法对电子显微镜图像进行分割，以跟踪用于催化和电子领域的薄膜中辐照引起的非晶前沿，为自动化电子显微镜提供指导。

电子显微技术中无监督分割的辐射诱导有序 - 无序相变

Unsupervised segmentation of irradiation$\unicode{x2010}$induced  order$\unicode{x2010}$disorder phase transitions in electron microscopy

Neural network quantum state (NNQS) has emerged as a promising candidate for
quantum many-body problems, but its practical applications are often hindered
by the high cost of sampling and local energy calculation. We develop a
high-performance NNQS method for \textit{ab initio} electronic structure
calculations. The major innovations include: (1) A transformer based
architecture as the quantum wave function ansatz; (2) A data-centric
parallelization scheme for the variational Monte Carlo (VMC) algorithm which
preserves data locality and well adapts for different computing architectures;
(3) A parallel batch sampling strategy which reduces the sampling cost and
achieves good load balance; (4) A parallel local energy evaluation scheme which
is both memory and computationally efficient; (5) Study of real chemical
systems demonstrates both the superior accuracy of our method compared to
state-of-the-art and the strong and weak scalability for large molecular
systems with up to $120$ spin orbitals.

我们开发了一种基于转换器的神经网络量子态方法，用于从头计算电子结构，并采用数据中心的并行化方案，平行化的批量采样策略，以及计算有效的局部能源计算方法。对化学体系的研究表明，我们方法的精度优于现有技术，并且在大分子系统上具有良好的强弱可扩展性。