ORCID
0000-0002-4603-3110
Keywords
Physics-informed neural networks, Helmholtz equation, computational electromagnetics, PINN, SIREN, electromagnetic wave propagation, mesh-free methods, scientific machine learning
Abstract
We present a physics-informed neural network (PINN) framework for solving the complex-valued two-dimensional Helmholtz equation with a localized Gaussian source and spatially varying permittivity. Starting from Maxwell’s equations, the frequency-domain scalar Helmholtz formulation under transverse electric (TE) polarization is derived and enforced directly within the neural network loss function. The model employs a sinusoidal representation network (SIREN) architecture to capture the oscillatory nature of wave solutions and incorporates the Sommerfeld radiation condition to impose open boundary conditions. Training is performed using a hybrid collocation strategy combined with a two-stage optimization procedure consisting of Adam followed by L-BFGS. Numerical experiments in free space and in the presence of a dielectric inclusion demonstrate physically consistent wave propagation, refraction, and scattering behavior. The resulting PINN achieves low residual error without requiring labeled simulation data and provides a mesh-free surrogate capable of rapid electromagnetic field evaluation after training. These results highlight the potential of physics-informed neural networks for frequency-domain computational electromagnetics and accelerated electromagnetic simulation.
Publication Date
4-9-2026
Original Citation
Panagiotakopoulos, Theodoros; Velissaris, Chris; and Rapsomanikis, Aristotelis-Nikolaos (2026). "Physics-Informed Neural Network Solution of the 2D Helmholtz Equation with a Gaussian Source."
Document Type
Paper
Copyright Status
Author retained
Rights
This work is licensed under a Creative Commons Attribution 4.0 International License.
College
College of Sciences
Location
Orlando (Main) Campus
Department
Physics
Accessibility Status
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STARS Citation
Panagiotakopoulos, Theodoros; Velissaris, Chris; and Rapsomanikis, Aristotelis Nikolaos, "Physics-Informed Neural Network Solution of the 2D Helmholtz Equation with a Gaussian Source" (2026). Faculty Scholarship and Creative Works. 1345.
https://stars.library.ucf.edu/ucfscholar/1345