Physics-Informed Neural Networks for Heat Transfer Problems

By Shengze Cai, Zhicheng Wang, Sifan Wang, Paris Perdikaris, G. Em Karniadakis. Journal of heat transfer, 2021

1,255 citations recorded by the source corpus.

Physics-informed neural networks (PINNs) have gained popularity across different engineering fields due to their effectiveness in solving realistic problems with noisy data and often partially missing physics. In PINNs, automatic differentiation is leveraged to evaluate differential operators without discretization errors, and a multitask learning problem is defined in order to simultaneously fit observed data while respecting the underlying governing laws of physics. Here, we present applications of PINNs to various prototype heat transfer problems, targeting in particular realistic conditions not readily tackled with traditional computational methods. To this end, we first consider forced and mixed convection with unknown thermal boundary conditions on the heated surfaces and aim to obtain the temperature and velocity fields everywhere in the domain, including the boundaries, given some sparse temperature measurements. We also consider the prototype Stefan problem for two-phase flow, aiming to infer the moving interface, the velocity and temperature fields everywhere as well as the different conductivities of a solid and a liquid phase, given a few temperature measurements inside the domain. Finally, we present some realistic industrial applications related to power electronics to highlight the practicality of PINNs as well as the effective use of neural networks in solving general heat transfer problems of industrial complexity. Taken together, the results presented herein demonstrate that PINNs not only can solve ill-posed problems, which are beyond the reach of traditional computational methods, but they can also bridge the gap between computational and experimental heat transfer.

Subfields: Aerospace Engineering, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1c5231abd89ddba21a80fe68146f531064f51f29

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Citations in the corpus

Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “, cyber-physical systems [223], chemistry [205], medical imaging [175], fluid mechanics [46], climate and weather [146]).”
Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “Moreover the governing equations in dimensionless form, including the Stokes equations, electric potential, and ion transport equations, are presented in DeepM&Mnets (Cai et al, 2021b).”
Physics‐Informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions (2021, methodology): “…DNNs and have been successfully applied to various problems in engineering and biology with applications including but not limited to heat transfer (Cai et al., 2021), solution of Navier-Stokes equations in fluid mechanics (Jin et al., 2021), high speed fluid flow (Mao et al., 2020) and solid…”
Physics-informed neural networks (PINNs) for fluid mechanics: a review (2021, methodology): “Following this work, PINNs were then applied to various ﬂows [10, 11,12,13,14,42,43,44,45,46,47,48,49], covering the applications on compressible ﬂows [13], biomedical ﬂows [14,42,50], turbulent convection ﬂows [48], free boundary and Stefan problems [47], etc.”
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? (2021, background): “Physics-informed neural networks (PINNs) [6] are among the most popular approaches with a wide variety of successful applications, including heat transfer problems [7], thrombus material properties [8], nano-optics [9], and fluid mechanics [10, 11].”