Document Type
Other
Publication Date
2025
Abstract
Physics-informed Neural Networks (PINNs) are an alternative approach to solving Partial Differential Equations. This study examines the Local Deep Galerkin Method (LDGM), and its application to the (2+1)-Dimensional Cahn-Hilliard Equation (2D-CH). The 2D-CH models phase separation. One application of this is to modeling biofilm. The LDGM is trained on a loss function that minimizes the sum of the squares of the residuals of the system of equations. The LDGM is compared to a numerical simulation based on the Finite Element Method. The results of this study show that LDGM does not produce accurate results for the 2D-CH equation for large amplitudes and frequencies of a cosine wave initial condition at an unacceptable error of about 80%.
Publisher
South Dakota State University
Rights
Copyright © 2025 Caden Fischer
Recommended Citation
Fischer, Caden, "The Local Deep Galerkin Method applied to the (2+1)-D Cahn-Hilliard Equation" (2025). Schultz-Werth Award Papers. 52.
https://openprairie.sdstate.edu/schultz-werth/52
