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 a purely data-driven model. In the former experiment, PSMs demonstrated significantly lower average root-mean-square errors across test datasets compared to a purely data-driven neural network, with reductions of 44 %, 48 %, and 94 % in predicting pressure, velocity, and temperature, respectively.

中文翻译：

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用于传输现象的基于物理的状态空间神经网络

这项工作介绍了基于物理的状态空间神经网络模型 (PSM)，这是一种在自主系统中实现实时优化、灵活性和容错的新颖解决方案，特别是在化学、生物医学和发电厂等运输主导的系统中。传统的数据驱动方法由于缺乏质量守恒等物理约束而存在不足； PSM 通过使用传感器数据训练深度神经网络并使用组件的偏微分方程 (PDE) 提供物理信息来解决此问题，从而产生物理约束的端到端可微正向动力学模型。通过两个计算机实验（加热通道和冷却系统回路），我们证明 PSM 提供了比纯粹数据驱动模型更准确的方法。在之前的实验中，与纯数据驱动的神经网络相比，PSM 在测试数据集中表现出显着较低的平均均方根误差，在预测压力、速度和温度方面分别降低了 44%、48% 和 94%。分别。