The Industrial Internet of Things (IIoT) is reshaping manufacturing,
industrial processes, and infrastructure management. By fostering new levels of
automation, efficiency, and predictive maintenance, IIoT is transforming
traditional industries into intelligent, seamlessly interconnected ecosystems.
However, achieving highly reliable IIoT can be hindered by factors such as the
cost of installing large numbers of sensors, limitations in retrofitting
existing systems with sensors, or harsh environmental conditions that may make
sensor installation impractical. Soft (virtual) sensing leverages mathematical
models to estimate variables from physical sensor data, offering a solution to
these challenges. Data-driven and physics-based modeling are the two main
methodologies widely used for soft sensing. The choice between these strategies
depends on the complexity of the underlying system, with the data-driven
approach often being preferred when the physics-based inference models are
intricate and present challenges for state estimation. However, conventional
deep learning models are typically hindered by their inability to explicitly
represent the complex interactions among various sensors. To address this
limitation, we adopt Graph Neural Networks (GNNs), renowned for their ability
to effectively capture the complex relationships between sensor measurements.
In this research, we propose physics-enhanced GNNs, which integrate principles
of physics into graph-based methodologies. This is achieved by augmenting
additional nodes in the input graph derived from the underlying characteristics
of the physical processes. Our evaluation of the proposed methodology on the
case study of district heating networks reveals significant improvements over
purely data-driven GNNs, even in the presence of noise and parameter
inaccuracies.

基于物理增强的图神经网络的软测量方法在区域供热网络案例研究中表现出显著的改进，即使在存在噪声和参数不准确性的情况下，这种方法克服了传统深度学习模型无法明确表示各种传感器之间复杂相互作用的限制。

基于物理增强的工业物联网软感知的图神经网络

Physics-Enhanced Graph Neural Networks For Soft Sensing in Industrial  Internet of Things

With the rise of deep learning, there has been renewed interest within the
process industries to utilize data on large-scale nonlinear sensing and control
problems. We identify key statistical and machine learning techniques that have
seen practical success in the process industries. To do so, we start with
hybrid modeling to provide a methodological framework underlying core
application areas: soft sensing, process optimization, and control. Soft
sensing contains a wealth of industrial applications of statistical and machine
learning methods. We quantitatively identify research trends, allowing insight
into the most successful techniques in practice.
We consider two distinct flavors for data-driven optimization and control:
hybrid modeling in conjunction with mathematical programming techniques and
reinforcement learning. Throughout these application areas, we discuss their
respective industrial requirements and challenges.
A common challenge is the interpretability and efficiency of purely
data-driven methods. This suggests a need to carefully balance deep learning
techniques with domain knowledge. As a result, we highlight ways prior
knowledge may be integrated into industrial machine learning applications. The
treatment of methods, problems, and applications presented here is poised to
inform and inspire practitioners and researchers to develop impactful
data-driven sensing, optimization, and control solutions in the process
industries.

利用深度学习技术，本研究旨在探索数据驱动感知、优化和控制在工艺产业中的应用及相关挑战，并提出基于统计和机器学习的混合建模方法与领域知识相结合的数据驱动方案。