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.
