DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning

Abstract

We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction problem with Dirichlet boundary conditions. The model is trained on solution data calculated using the Alternating direction implicit method. We show the model's ability to predict the solution from any combination of seven variables: the starting time step of the solution, initial condition, four boundary conditions, and a combined variable of the time step size, diffusivity constant, and grid step size. To improve speed, we exploit our model capability to predict the solution of the Time-dependent PDE after multiple time steps at once to improve the speed of solution by dividing the solution into parallelizable chunks. We try to build a flexible architecture capable of solving a wide range of partial differential equations with minimal changes. We demonstrate our model flexibility by applying our model with the same network architecture used to solve the transient heat conduction to solve the Inviscid Burgers equation and Steady-state heat conduction, then compare our model performance against related studies. We show that our model reduces the error of the solution for the investigated problems.