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[2509.12483] Comparative Analysis of Wave Scattering Numerical Modeling Using the Boundary Element Method and Physics-Informed Neural Networks
Summary
This article compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving wave scattering problems, highlighting their performance in terms of accuracy and computation time.
Why It Matters
Understanding the comparative performance of BEM and PINNs is crucial for researchers in computational physics and machine learning, as it informs the choice of methods for solving complex wave propagation problems, potentially leading to more efficient modeling techniques.
Key Takeaways
- BEM and PINNs were evaluated for solving the Helmholtz equation in wave scattering.
- BEM requires significantly less computational time for assembly compared to PINNs during training.
- Once trained, PINNs provide faster evaluation times than BEM for interior points.
- Hyperparameter tuning is essential for optimizing PINN performance.
- The study establishes a framework for comparing numerical modeling techniques in wave propagation.
Computer Science > Machine Learning arXiv:2509.12483 (cs) [Submitted on 15 Sep 2025 (v1), last revised 20 Feb 2026 (this version, v3)] Title:Comparative Analysis of Wave Scattering Numerical Modeling Using the Boundary Element Method and Physics-Informed Neural Networks Authors:Oscar Rincón-Cardeno, Gregorio Pérez Bernal, Silvana Montoya Noguera, Nicolás Guarín-Zapata View a PDF of the paper titled Comparative Analysis of Wave Scattering Numerical Modeling Using the Boundary Element Method and Physics-Informed Neural Networks, by Oscar Rinc\'on-Cardeno and 3 other authors View PDF HTML (experimental) Abstract:This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods under the same conditions. We solve the Helmholtz equation using BEM and PINNs for the same scattering problem. PINNs are trained by minimizing the residual of the governing equations and boundary conditions with their configuration determined through hyperparameter optimization, while BEM is applied using boundary discretization. Both methods are evaluated in terms of solution accuracy and computation time. We conducted numerical experiments by varying the number of boundary integration points for the BEM and the number of hidden layers and neurons per layer for the PINNs. We performed a hyperparameter tuning to identify an adequat...