This work introduces Physics-informed State-space neural network Models
(PSMs), a novel solution to achieving real-time optimization, flexibility, and
fault tolerance in autonomous systems, particularly in transport-dominated
systems such as chemical, biomedical, and power plants. Traditional data-driven
methods fall short due to a lack of physical constraints like mass
conservation; PSMs address this issue by training deep neural networks with
sensor data and physics-informing using components' Partial Differential
Equations (PDEs), resulting in a physics-constrained, end-to-end differentiable
forward dynamics model. Through two in silico experiments - a heated channel
and a cooling system loop - we demonstrate that PSMs offer a more accurate
approach than purely data-driven models.
Beyond accuracy, there are several compelling use cases for PSMs. In this
work, we showcase two: the creation of a nonlinear supervisory controller
through a sequentially updated state-space representation and the proposal of a
diagnostic algorithm using residuals from each of the PDEs. The former
demonstrates the ability of PSMs to handle both constant and time-dependent
constraints, while the latter illustrates their value in system diagnostics and
fault detection. We further posit that PSMs could serve as a foundation for
Digital Twins, constantly updated digital representations of physical systems.

这项工作介绍了物理信息化状态空间神经网络模型（PSMs），它是实现自主系统中的实时优化、灵活性和容错性的一种新颖解决方案，特别适用于化学、生物医学和电力等以传输为主的系统。通过两个硅橡胶实验 —— 加热通道和制冷系统环路，我们证明了 PSMs 比纯数据驱动模型提供了更准确的方法。除了准确性，PSMs 还具有几个引人注目的用途：通过顺序更新的状态空间表示创建非线性监控控制器以及使用来自 PDE 的残差提出诊断算法。我们进一步提出 PSMs 可以作为数字孪生的基础，不断更新的物理系统的数字表示。