Physics-Informed Neural Networks for Full-Field Transient Temperature Reconstruction in Dimension-Reduced Fin Systems with Sparse Data

Abstract

Heat transfer through extended surfaces (fins) is widely used in engineering applications ranging from portable electronic devices to spacecraft to improve heat dissipation. Accurate prediction of the temperature distribution along the fins is essential to optimize them for desired applications. This study presents a Physics-Informed Neural Network (PINN) approach to solve the transient fin equation.

In this study, the neural network predicts the temperature distribution by satisfying the governing physical laws and the sparse temperature sensor data, representing the most practical applications where embedded sensor probes gather data and feed it to the appropriate controller to drive the device.

This study emphasizes the use of PINN rather than conventional numerical methods, which need spatial discretization of the computational domain through mesh generation. The prediction accuracy in numerical methods strongly depends on the optimization of the quality and resolution of the mesh. The mesh optimization algorithm in a numerical solver plays an important role in mesh quality. This approach can increase the computational cost for complex geometries and is not suitable for real-time heat tracking and optimization.

In contrast, PINNs employ a neural network to estimate the solution function from the governing physical laws and to reduce the dependency on conventional mesh-based discretization. Furthermore, PINNs have the potential for real-time heat tracking and optimization, thanks to modern neural processing units (NPUs). Training PINNs can be computationally expensive; however, this study presents a novel approach to developing lightweight PINN models that can be trained effectively using limited sparse datasets.

This study developed a three-dimensional straight transient fin model to generate numerical simulation data and considered it as a reference dataset. The three-dimensional model was simplified to a one-dimensional model for the PINN approach. The PINN model predicted the transient temperature field with sparse data while minimizing loss functions, and the predictions were com- pared to the reference values. The results show stable convergence and high prediction accuracy of the reduced-dimension PINN model compared to the three-dimensional transient fin model. Furthermore, this study shows the effectiveness of PINN under different values of the convective heat transfer coefficient (h) and noisy environments.

This study demonstrates the high accuracy of the PINN for transient fin problems by comparing the results with data from virtual sensors obtained from simulations of an industrial numerical solver. To do this, this study presents a novel approach of reducing the dimensions and developing training algorithms. The proposed approach demonstrates that PINNs can provide an accurate solution without conventional mesh discretization for transient fin problems, serve as a competitive alternative to classical numerical solvers, and can be a computationally cost-effective solution for complex geometries.