Neural Network-Based Solutions for the Linearized Euler Equations in Outdoor Sound Propagation

Kurzfassung

The Linearized Euler Equations (LEE) are a system of partial differential equations that provide a framework for modeling outdoor acoustic wave propagation, capturing atmospheric and topographic effects. Solving LEE using traditional numerical methods demands fine spatial and temporal resolutions, leading to high computational costs over large domains. This study uses established neural network approaches to solve LEE and evaluates their performance and scalability for outdoor acoustic wave propagation. Included approaches are Physics-Informed Neural Networks (PINNs) and the sampled network-based Extreme Learning Machine Ordinary Differential Equations (ELM-ODE). We use a SIREN-based architecture in our PINNs for wave-like solutions. In the 1D case, PINNs achieved higher accuracy but required significantly more training time due to the complexity of training over a spatiotemporal domain. Meanwhile, ELM-ODE provided competitive accuracy with much lower computational cost. In the 2D case, ELM-ODE again showed computational advantages over SIREN-PINNs while delivering great accuracy. However, its scalability is constrained by the coupled velocity–pressure matrix, which increases costs in cases like outdoor noise mapping, where velocity data eventually are unused. Addressing boundary conditions, such as frequency-dependent impedance, remains a challenge.