Physics-informed State-space Neural Networks for Transport Phenomena
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914917080104960 |
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| author | Dave, Akshay J. Vilim, Richard B. |
| author_facet | Dave, Akshay J. Vilim, Richard B. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_12211 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Physics-informed State-space Neural Networks for Transport Phenomena Dave, Akshay J. Vilim, Richard B. Machine Learning Systems and Control Computational Physics Fluid Dynamics 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. |
| title | Physics-informed State-space Neural Networks for Transport Phenomena |
| topic | Machine Learning Systems and Control Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2309.12211 |