Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks - Yufan Pan; Ke Zhang; Ji Zhang; Ning Mei (Eng)
This study investigates a simulation-based approach to the inverse problem of two-dimensional steady-state heat conduction in flat plates by employing Physics-Informed Neural Networks (PINNs). The primary objective is to reconstruct the temperature field and deduce unknown boundary conditions using limited labeled data sourced from conventional numerical methods. This work specifically validates the methodology using simulated data with known original conditions, rather than addressing truly unknown boundary conditions in real-world scenarios. By leveraging PINNs, the approach integrates physical laws with data-driven learning, facilitating the efficient inversion of boundary conditions and precise reconstruction of the temperature field. Within a temperature range of 10 °C to 40 °C, the method consistently achieves an average relative error of less than 10% and maintains an absolute error within 1 °C across the computational domain. By optimizing the distribution of sample points without increasing their quantity, the average relative error is further reduced by approximately 1%, thereby enhancing inversion accuracy. Additionally, implementing an adaptive weight adjustment strategy, based on learning rate annealing, further refines the method, reducing the maximum absolute error by 0.4 °C and the average relative error by 2% when compared to traditional PINNs. This research demonstrates the capability of PINNs to provide a rapid and effective solution for inverse heat conduction problems, establishing a foundation for their potential application in addressing complex inverse heat transfer challenges.