This work proposes a Physics-informed Neural Network framework with Graph
Embedding (GPINN) to perform PINN in graph, i.e. topological space instead of
traditional Euclidean space, for improved problem-solving efficiency. The
method integrates topological data into the neural network's computations,
which significantly boosts the performance of the Physics-Informed Neural
Network (PINN). The graph embedding technique infuses extra dimensions into the
input space to encapsulate the spatial characteristics of a graph while
preserving the properties of the original space. The selection of these extra
dimensions is guided by the Fiedler vector, offering an optimised pathologic
notation of the graph. Two case studies are conducted, which demonstrate
significant improvement in the performance of GPINN in comparison to
traditional PINN, particularly in its superior ability to capture physical
features of the solution.

本文提出了一种基于图嵌入的物理信息神经网络框架（GPINN），使用拓扑空间而非传统的欧几里得空间来执行 PINN，以提高问题解决效率。该框架将拓扑数据集成到神经网络的计算中，显著提高了 PINN 的性能。通过 Fiedler 向量引导选择额外的维度，将额外的维度注入输入空间，以封装图的空间特征，同时保留原空间的属性。此外，本文进行了两个案例研究，证明 GPINN 在与传统 PINN 相比，特别是在捕获解的物理特征方面具有显著的性能优势。

GPINN: 带有图嵌入的物理知识神经网络

GPINN: Physics-informed Neural Network with Graph Embedding

This paper introduces a novel method for merging open-domain terminological
knowledge. It takes advantage of the Region Connection Calculus (RCC5), a
formalism used to represent regions in a topological space and to reason about
their set-theoretic relationships. To this end, we first propose a faithful
translation of terminological knowledge provided by several and potentially
conflicting sources into region spaces. The merging is then performed on these
spaces, and the result is translated back into the underlying language of the
input sources. Our approach allows us to benefit from the expressivity and the
flexibility of RCC5 while dealing with conflicting knowledge in a principled
way.

本文提出了一种新的方法来合并开放领域的术语知识，该方法利用了区域连接演算（RCC5）。我们首先将多个潜在冲突来源提供的术语知识信任地转化为区域空间，然后在这些空间上执行合并，并将结果转换回输入源的底层语言。我们的方法允许我们从 RCC5 的表达能力和灵活性中受益，同时以原则性的方式处理冲突知识。