Physics-informed neural networks for simulating 1D and 2D heat transfer equations

Abstract

In this study, we present the simulation of 1D and 2D heat transfer equations using physics- informed neural networks (PINNs) to predict temperature distributions over time. PINNs leverage

the underlying physical laws governing heat diffusion, integrating these principles directly into the neural network training process. This approach ensures accurate, physically consistent simulations even with limited data. We applied PINNs to solve the heat equation in both one-dimensional and two-dimensional domains, demonstrating their efficacy in capturing the temporal evolution of temperature profiles. The simulations were conducted for various time intervals, highlighting the model's ability to generalize across different temporal scales. PINNs offers a simpler and more efficient computational process compared to traditional numerical and analytical methods, particularly for higher-dimensional equations. This work underscores the potential of PINNs to solve complex physics-based problems with greater efficiency and less complexity, highlighting their promise as powerful tools in engineering and scientific applications.