Physics-informed State-space Neural Networks for Transport Phenomena
This addresses the problem of real-time optimization and fault tolerance in autonomous systems like chemical plants, offering an incremental improvement over existing physics-informed methods.
The paper tackles the lack of physical constraints in data-driven models for transport phenomena by introducing Physics-informed State-space neural network Models (PSMs), which integrate PDEs with neural networks, resulting in significantly lower errors—e.g., 94% reduction in temperature prediction—compared to purely data-driven approaches.
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. Beyond accuracy, PSMs demonstrate a compelling multitask capability, making them highly versatile. In this work, we showcase two: supervisory control of a nonlinear system through a sequentially updated state-space representation and the proposal of a diagnostic algorithm using residuals from each of the PDEs. The former demonstrates PSMs' ability to handle 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.