New Perspectives of Solution of Heat Equation Using Neural Networks and Jensen’s Inequality

Abstract

In this study, we used Physics-Informed Neural Networks (PINNs) to solve the 1D, 2D, and 3D heat equation. To enhance training stability and accuracy, we replaced Jensen’s inequality as the loss function with more traditional methods such as Mean Square Error (MSE). We aimed to demonstrate that it is possible for PINNs to efficiently solve the heat equation with minimal data. In order to implement the model, we used a number of libraries, such as TensorFlow and Keras for creating the neural networks and NumPy, SciPy, and Matplotlib for managing the data and displaying the outcomes.