Comparative Evaluation of Periodic Boundary Condition Approaches in PINNs

Paper in proceeding, 2025

This study investigates the enforcement of periodic boundary conditions (PBCs) in physics-informed neural networks (PINNs), a key challenge in fluid dynamics. Both soft and hard constraint approaches are examined, comparing their theoretical foundations and practical implications. For soft PBCs, the One-Period approach is shown to be the most effective, preventing convergence to suboptimal solutions. For hard PBCs, various functions are evaluated. Additionally, the required number of neurons in the periodic layer is analyzed, confirming that at least two neurons are necessary for proper optimization and convergence across all tested functions. The linear surface wave problem serves as a benchmark, providing a comprehensive assessment of these strategies. The findings offer valuable insights optimal design choices for PINNs in periodic problems, guiding their application in fluid dynamics and related fields.