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.

翻译：本文提出物理信息状态空间神经网络模型（Physics-informed State-space neural network Models, PSMs），这是一种实现自主系统实时优化、灵活性和容错性的新型解决方案，尤其适用于化工、生物医学和发电厂等输运主导系统。传统数据驱动方法因缺乏质量守恒等物理约束而存在局限性；PSMs通过利用传感器数据训练深度神经网络，并采用组件的偏微分方程（PDEs）进行物理信息注入，从而构建具有物理约束的端到端可微前向动力学模型。通过两项计算实验（加热通道与冷却系统回路），我们证明了PSMs比纯数据驱动方法具有更高的准确性。除精度优势外，PSMs还有若干引人注目的应用场景。本文展示其中两项：一是通过顺序更新的状态空间表示构建非线性监督控制器，二是利用各PDE残差提出诊断算法。前者展示了PSMs处理恒定与时间依赖约束的能力，后者则体现了其在系统诊断与故障检测中的价值。我们进一步指出，PSMs可作为数字孪生（Digital Twins）的基础——即持续更新的物理系统数字表征。