NeuroDiffeq: Implementing Artificial Neural Networks to Solve 2D Helmholtz Equations

Abstract

This paper investigates the application of artificial neural networks (ANNs) for solving two-dimensional Helmholtz equations using the NeuroDiffEq framework. Based on PyTorch, NeuroDiffEq enables mesh-free approximations of PDE solutions by minimizing the residuals of the differential equation and its boundary conditions through automatic differentiation. The proposed method integrates a trial analytical solution (TAS) to enforce boundary constraints and uses a feedforward neural network trained via the Adam optimizer. We evaluate the model on several benchmark Helmholtz problems and report mean squared errors (MSE) as low as 1.08 10