Physics informed neural network-based framework for two-dimensional phase change problems

Abstract

In this work, we propose a framework to solve two-dimensional phase change problems with arbitrary shaped interfaces using physics-informed neural network. These problems are characterized by moving interfaces driven by the heat flux distribution during the phase change process. We model the phase change using a diffuse interface enthalpy formulation, where the interface has a finite width and phase change occurs over a specified temperature range. A loss function only based on the temperature field is formulated, by reframing the latent enthalpy change in terms of the temperature field and phase change temperature range. This allows us to predict the transient temperature field and interface position with the help of a simple PINN architecture consisting of a single neural network. Further the loss function does not consist of any terms related to the interface condition, making the overall implementation simple in nature. We demonstrate the effectiveness of our approach by solving a series of problems with different combinations of boundary conditions and heat sources without using any prior data and illustrate how the proposed framework can capture solution of phase change problems with arbitrary-shaped dynamic interfaces.