Physics-informed State-space Neural Networks for Transport Phenomena

• Published in: arXiv.org
• Main Authors: Dave, Akshay J, Vilim, Richard B
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.12.2023
• Subjects: Algorithms; Artificial neural networks; Computer Science - Learning; Computer Science - Systems and Control; Constraints; Cooling systems; Digital twins; Fault detection; Fault tolerance; Model accuracy; Neural networks; Nonlinear control; Optimization; Partial differential equations; Physics; Physics - Computational Physics; Physics - Fluid Dynamics; Power plants; State space models; Supervisory control; Time dependence; Transport phenomena
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2309.12211

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.